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Quantum communication complexity advantage implies violation of a Bell inequality
Edited by Anton Zeilinger, University of Vienna, Vienna, Austria, and approved January 7, 2016 (received for review April 22, 2015)
This article has a correction. Please see:
For many communication complexity problems the quantum strategies, distinguished by using Bell nonlocal correlations, provide exponential advantage over the best possible classical strategies. Conversely, for any Bell nonlocal correlations there exists a communication complexity problem that is solved more efficiently using the former. Despite many efforts, there were only two problems for which one could certify that any strategy that outperforms the classical one must harbor Bell nonlocal correlations. We prove that any large advantage over the best known classical strategy makes use of Bell nonlocal correlations. Thus, we provide the missing link to the fundamental equivalence between Bell nonlocality and quantum advantage.
We obtain a general connection between a large quantum advantage in communication complexity and Bell nonlocality. We show that given any protocol offering a sufficiently large quantum advantage in communication complexity, there exists a way of obtaining measurement statistics that violate some Bell inequality. Our main tool is port-based teleportation. If the gap between quantum and classical communication complexity can grow arbitrarily large, the ratio of the quantum value to the classical value of the Bell quantity becomes unbounded with the increase in the number of inputs and outputs.
The key element that distinguishes classical from quantum information theory is quantum correlations. The first attempt to quantify their strength was quantitatively expressed in Bell's theorem (1). They are similar to classical correlations in that one cannot take advantage of them to perform superluminal communication, yet every attempt to explain such correlations from the point of view of classical theory—namely, to find a local hidden variable model—is impossible. For a long time the existence of quantum correlations was merely of interest to philosophically minded physicists and was considered an exotic peculiarity, rather than a useful resource for practical problems in physics or computer science. This has changed dramatically in recent years—it became apparent that quantum correlations can be used as a resource for a number of distributed information processing tasks (2⇓–4), producing surprising results (5, 6).
One area where using quantum correlations has wide-reaching practical implications is communication complexity. A typical instance of a communication complexity problem features two parties, Alice and Bob, who are given binary inputs x and y. They wish to compute the value of by exchanging messages between each other. The minimum amount of communication required to accomplish the task by exchanging classical bits (with bounded probability of success) is called classical communication complexity, denoted as .
There are two ways to account for the communication complexity of computing a function when we want to make use of quantum correlations. In the first one, Alice and Bob share any number of instances of the maximally entangled state beforehand and are allowed to exchange classical bits to solve the problem. Another approach is to have no preshared entanglement, but instead allow Alice and Bob to exchange qubits. The latter type of protocol can always be converted to the former with preshared entanglement and classical communication. We denote the quantum communication complexity of computing the function (with bounded probability of success) by .
For a large number of problems, the respective quantum communication complexity is much lower compared with its classical counterpart (4, 7). In such cases, we say that there exists a quantum advantage for communication complexity. In other words, one achieves a quantum advantage if the quantum communication complexity of the function is lower than its corresponding classical communication complexity.
One of the most striking example of quantum advantage is the famous Raz problem (5, 8), where quantum communication complexity is exponentially smaller than classical. Another example is the "hidden matching" problem for which the quantum advantage leads to one of the strongest possible violations of the Bell inequality (9). The latter inequality plays an important role in detecting quantum correlations and certifying the genuinely quantum nature of resources at hand. Previously, to obtain an unbounded violation of a particular Bell inequality one resorted to problems with the exponential quantum advantage. Here, we show that one can achieve the same result, using only polynomial quantum advantage.
As a matter of fact, the very first protocols offering quantum advantage were based on a quantum violation of certain Bell inequalities (6). It was even shown that for a very large class of multiparty Bell inequalities, correlations that violate them lead to a quantum advantage (perhaps, for a peculiar function) (10). This indicates that Bell nonlocality often leads to a quantum advantage. However, there are more and more communication protocols that offer a quantum advantage, but, nevertheless, they are not known to violate any Bell inequality.
It has long been suspected (6) that quantum communication complexity and Bell nonlocality are the two sides of the same coin. Although it is possible to convert a Bell nonlocality testing experiment to the communication complexity instance, the reverse has been known only for some particular examples. The question is whether this relationship holds in general, namely, Is quantum communication inherently equivalent to Bell nonlocality when solving communication complexity problems?
Until now, there were only two concrete examples where one could certify quantum correlations in the context of communication complexity by providing a quantum state and a set of measurements whose statistics violate some Bell inequality. The first case is the "hidden matching" problem and the second one is a theorem, which states that a special subset of protocols that provide quantum advantage also implies the violation of local realism (6). To get the violation of Bell inequalities obtained from the examples above, one had to perform an involved analysis that relied on a problem-specific set of symmetries. Thus, such an approach cannot be generalized to an arbitrary protocol for achieving a quantum advantage in the communication complexity problem.
In this paper, we show that given any (sufficiently large) quantum advantage in communication complexity, there exists a way of obtaining measurement statistics that violate some linear Bell inequality. This completely resolves the question about the equivalence between the quantum communication and Bell nonlocality: Whenever a protocol computes the value of the function better than the best classical protocol, even with a gap that is only quadratic, then there must exist a Bell inequality that is violated.
We provide a universal method that takes a protocol that achieves the quantum advantage in any single- or multiround communication complexity problem and uses it to derive the violation of some linear Bell inequality. This method can be generalized to a setting with more than two parties. Our Bell inequalities lead to a so-called unbounded violation (11): The ratio of the quantum value to the classical value of the Bell quantity can grow arbitrarily large with the increase of the number of inputs and outputs, whenever the ratio of and grows too. In particular, an exponential advantage leads to an exponential ratio.
Our method consists of two parts. In the first part, we use the quantum protocol based on the given communication complexity game to construct a set of quantum measurements on a maximally entangled state The central ingredient of our construction is the recently discovered port-based teleportation (12, 13). In the second part, given a protocol that computes a function f by using qubits, and the optimal classical error probability achievable with bits, we construct the corresponding linear Bell inequality that is subsequently violated by the above quantum measurements.
For one-way communication complexity problems we develop a much simpler method that is based on the remote state preparation and results in a nonlinear Bell inequality.
Quantum Communication Complexity Protocol
We start by defining a general quantum multiround communication protocol. Two parties, Alice and Bob, receive inputs and according to some distribution μ and their goal is to compute the function by exchanging qubits over multiple rounds. We further use subscripts for the system names to denote the round number. The parties proceed as follows:
i) Alice applies on her local state and sends to Bob. In general, may be entangled with , which remains with Alice.
ii) Bob performs on the state . Then he sends back the system to Alice, keeping .
iii) Parties repeat steps i and ii for rounds. In the last round, instead of communicating back to Alice, Bob measures the observable and outputs the value of the function f. The observable acts on the system and Bob's memory .
The above protocol may be transformed to the form where a one-qubit system is exchanged between Alice and Bob at any round. To achieve this, we split the Q-qubit message from Alice to Bob (or vice versa) into Q rounds of one-qubit transmission and modify the protocol as follows. We start from the initial state, which has the form[1]where and describe the memory registers that belong to Alice and Bob, respectively. The state , initially in state with Alice, is a one-qubit system that is used for message passing from Alice to Bob and vice versa. In each round, Alice applies to , and Bob applies to . In the last round, instead of applying a unitary transformation, Bob performs a measurement. One may view unitaries and as controlled gates acting on the memory with the one-qubit register acting as a control. This implies that for given x, in round i the state of Alice's memory is spanned on at most orthogonal vectors. This observation will be crucial for the construction of a compressed-memory quantum protocol. Thus, we can transform any given protocol that requires Q qubits of communication into one that makes use of one-qubit exchanges.
From an Arbitrary Protocol to a Compressed-Memory Protocol
One shortcoming of the above protocols is that both players possess a local memory, possibly entangled with the message, which can span an arbitrary number of qubits and therefore could be much too big to properly handle in other parts of our construction. We solve this problem by converting an arbitrary protocol, as described above, to a protocol where we can upper bound the maximum size of the local memory.
The following proposition, which is a consequence of the Yao–Kremer lemma (3, 14), shows that it is possible to compress the parties' local memory each step and that therefore the size of the local memory can be assumed to be at most the total communication. We include the proof in Supporting Information, section IV.
Proposition 1.
For any Q-qubit quantum communication protocol (without prior entanglement) there exists a Q-qubit quantum communication protocol for which Alice and Bob can encode their local memory on at most Q qubits each.
Quantum Measurements from the Quantum Communication Complexity Protocol
We now show how to convert a multiround compressed-memory protocol for computing , which gives a quantum advantage to the violation of a linear Bell inequality. There exist two different protocols to achieve this. The first protocol is based on the recently introduced method of port-based teleportation, which we briefly review in the next section. The second method, discussed at the end of this paper, relies on remote state preparation (15). We base our construction on the port-based teleportation because unlike the remote state preparation it is easily extendible to the multiround protocol and also gives rise to a linear Bell inequality.
Port-Based Teleportation
In deterministic port-based teleportation, the two parties share N pairs of maximally entangled qudits , each of which is called a "port." To transmit the state , the sender performs the square-root teleportation measurement given by a set of positive operator valued measure (POVM) elements (precisely defined in equation 27 of ref. 13) on all of the systems , , obtaining the result . Then, he or she communicates z to the receiver who traces out the subsystems and remains with the teleported state in the subsystem . Teleportation always succeeds and the fidelity of the teleported state with the original is . The cost of the classical communication from sender to receiver is equal to . The distinctive feature of this protocol is that unlike with original teleportation, it does not require a correction on the receiver's side.
Constructing Quantum Measurements
Using port-based teleportation we can now construct the relevant quantum measurements. Parties start with the initial state [1] and perform the following protocol:
i) Alice applies on her local state . She obtains the state of size , which is teleported to Bob at once, using ports each of dimension . This consumes ports. Alice does not communicate the classical teleportation outcomes , with to Bob.
ii) Bob applies the local unitary to each of the ports (he does not know the value of ) and teleports each of the states one-by-one by applying the teleportation measurement using ports each of the dimension , where . This consumes ports. Bob keeps the set of teleportation outcomes , , where for each , .
iii) Parties repeat steps i and ii for rounds.
At the end of the protocol we obtain the set of measurements that map the generic communication protocol into the set of correlations,[2]where are the final teleportation measurements in round r on Bob's side. An important feature of this construction is that all of the quantum measurements are performed simultaneously but the classical information exchange happens sequentially. A single round of the protocol is depicted in Fig. 1 and the entire protocol is depicted in Fig. 2.
Simulating the Quantum Protocol
The last part of the puzzle is a method of simulating the compressed-memory quantum protocol, using the above correlations and classical communication.
Lemma 1.
Given a protocol for computing f that uses Q qubits of communication and achieves the success probability , , one can simulate it using correlations [2] and bits of classical communication with the success probability .
Having access to correlations [2], Alice and Bob exchange their respective outcomes of the teleportation measurements that amount to bits of communication. This finalizes the port-based teleportation and thus simulates the corresponding quantum protocol. After exchange, Bob returns , where L denotes the last index that he received from Alice.
The above protocol is equivalent to rounds of port-based teleportation used for the compressed-memory protocol. Because by the compression of Proposition 1 for every round i the dimension of the teleported state is at most (the message is encoded in 1 qubit and the local memories are encoded in Q qubits each), we set so that the fidelity of teleportation on each step is . Then the protocol has success probability , where is the success probability of the original quantum protocol. Bounding the number of rounds r by the total amount of quantum communication Q, we get . Thus, the total amount of classical communication is bounded above by .
Construction of a Bell Inequality and Its Violation
Let us sum up the whole construction. First, we start with a quantum multiround protocol to compute f that uses quantum communication and no shared entanglement. This protocol requires Q qubits of communication and achieves . In this protocol, Alice and Bob may use an arbitrary amount of local quantum memory between rounds. Second, we convert it to the protocol with compressed local quantum memory, where the latter can be encoded in Q qubits. The compressed protocol is then used to obtain correlations in the form [2]. These correlations together with classical communication are used to recover the original communication complexity protocol that computes f. This protocol uses bits of classical communication and achieves success probability .
Now, if for a function there exists a gap between and with for the classical communication complexity protocol, and —then we observe the quantum violation of the Bell inequality of the form[3]where μ is a probability measure on , the set denotes the set of all paths from the root to the leaves of length of the tree formed by the subsequent outputs of Alice and Bob in the protocol, and is the marginal probability that comes from summing over all indexes that do not explicitly appear in the path q (Fig. 3). With the exception of the last level, every node on the ith level has children that correspond to the outcome of the ith round of teleportation. The index of the first node in the path corresponds to the state being on Alice's side and each subsequent index corresponds to the state being either on Alice's or on Bob's side in the alternating manner. The leaves of the tree correspond to the outcomes of Bob's binary observable, which is his guess of the value of the function . (Note that in the Bell inequality, only special outputs appear—those given by the paths of length from the root to the leaves—whereas in general, outputs will be given by all sequences composed of choosing one node from every level.)
The Bell inequality [3] is the central quantity of this paper. The left-hand side of the inequality constitutes the maximal success probability of guessing the value of f that can be achieved with the correlations of the form [2]. If this success probability turns out to be greater than the maximal success probability attained by the best classical protocol (the right-hand side of the inequality), this implies that correlations [3] reveal Bell nonlocality.
Large Violation of a Bell Inequality from Communication Complexity
We now show how to combine the above ingredients to get the main result: Whenever , we obtain an unbounded violation of the Bell inequality—the ratio of the quantum to the classical value of our Bell inequality grows arbitrarily when we increase the number of inputs and outputs (6, 9, 11, 16⇓–18).
To state and proof the main theorem we summarize the above results in the following sequence of steps:
i) Given a quantum protocol with advantage that uses Q bits of communication and achieves , we convert it (using Proposition 1) to the memoryless protocol that uses bits of communication and achieves the same success probability.
ii) From the memoryless protocol using measurements and quantum state we obtain the set of quantum correlations .
iii) Using and bits of classical communication, we obtain a new protocol that achievesRecall that all of the above measurements are done simultaneously, but the exchange of the corresponding classical information happens sequentially.
iv) We turn protocol into a Bell inequality. To this end, we consider a general construction of Bell inequality given any function and a protocol P that uses communication and correlations. Namely, denote to be a guess of determined by the protocol for given inputs and outputs . Then, consider the probability of success of guessing the correct value of the function f parameterized by the correlations R,[4]
where is the indicator function. Our Bell inequality will simply be a shifted value of guessing probability
v) We consider the behavior of the above Bell inequality on classical correlations as a function of the amount of communication used by . To this end we apply Lemma 3 (proved in Supporting Information, section I), which states that given an arbitrary protocol P that uses bits of communication, we have
We apply it to our protocol .
Our main claim is contained in Theorem 1:
Theorem 1.
Suppose two parties can compute a function f, using the protocol P with Q qubits of communication and the success probability . Then there exist a quantum correlation and a Bell inequality such that[6]where is the classical communication complexity of f with probability , and stands for arbitrary classical correlation.
Theorem 1 implies that if is sufficiently smaller than C (i.e., when we have a sufficiently large quantum advantage in communication complexity), then we obtain violation of a Bell inequality.
Given the protocol P of computing f with success probability (where we set ) while using Q qubits of communication, we consider protocol from item iii, which uses bits of communication with the same probability of success. If applied to correlations of item ii and using Lemma 1 above, it achieves the success probability . Thus, the Bell inequality constructed in item v evaluated on gives[7]The next step is to check the value of the same Bell inequality on classical correlations . To this end, we apply item v with , and , obtaining that for any classical correlations [8]We put together Eqs. 7 and 8, obtaining the required bound for the ratio of Bell value on our particular quantum correlation and arbitrary classical correlation :[9]
For the right-hand side becomes large, implying large violation of a Bell inequality. The diagrammatic proof of Theorem 1 is depicted in Fig. 4.
We provide several examples to demonstrate the power of our result.
Both of the examples are based on an explicit communication complexity problem called "vector in subspace" that was first introduced in ref. 5. In this problem, Alice and Bob receive the n-dimensional vector v and the description of -dimensional subspace H, respectively, with the promise that either or . The aim of the game is to determine which subspace v belongs to by exchanging messages between the parties. We consider two variants of the problem below.
Vector in Subspace Problem with One-Way Communication.
In this protocol, there is only one round of communication from Alice to Bob. Also, the local memory is not used. The deterministic quantum protocol requires qubits of communication (where n is the length of the vector in the problem), whereas the classical communication complexity is (8).
Knowing the quantum protocol P explicitly, we obtain a stronger Bell inequality because we do not need to invoke any approximations. Using bits of communication and correlations [2], we can achieve the quantum success probability of , whereas the classical protocol using the same amount of communication achieves , where , for some constant A. Thus, the ratio of quantum to classical values of the Bell inequality given in Theorem 1 is[10]where we use when it does not lead to ambiguity.
Vector in Subspace Problem with Two-Way Communication [Raz Original Problem (5)].
In this protocol, Alice sends Bob a quantum state of size (where n is the length of the vector in the problem) and then receives a state of the same size. As in the previous example, the parties do not use any local memory. There exists a deterministic quantum protocol for this problem. The classical communication complexity is . But using only qubits of communication and correlations [2], we get . The classical protocol using the same amount of communication achieves , where , for some constant A. Thus, the ratio of quantum to classical Bell values is[11]
One-Way Communication Complexity Problems.
We now detail the scenario when Alice is allowed to send a single message to Bob to introduce a very different approach to obtain the violation of a Bell inequality. In this case, state preparation protocol on Alice's side followed by the measurement of a quantum state by Bob will suffice. Also, there is no need for the local quantum memory on either side because one does not have to preserve the state of the communication protocol. Therefore, the role of the port-based teleportation is played by the remote state preparation.
One marked difference of this approach is that it consumes a significantly smaller amount of entanglement. Also, in this setting, we obtain the nonlinear Bell inequality that explicitly features the probability of Bob guessing the communication from Alice—something that is not possible using the method that relies on the port-based teleportation.
We first outline the remote state preparation protocol and then construct the relevant Bell inequalities below.
Remote State Preparation.
In the remote state preparation, Alice and Bob share a maximally entangled qudit state . Alice wants to prepare a known quantum state on Bob's side by acting only on her share of the qudit, requiring no postprocessing on his side. To achieve this, she performs a measurement with elements , where is a conjugation of in the computational basis, on her part of , followed by the communication of the classical outcome to Bob if she measured (we denote this outcome as 1). This protocol has a very low probability of success, 1/d. We discuss the techniques to amplify it in Supporting Information, section II.
Applying the remote state preparation protocol to our communication complexity problem, we obtain the correlations[12]where are the POVM elements from the remote state preparation and describes Bob's measurements on the shared state . In the current setup, the number of the binary observables of Alice and Bob is equal to the number of inputs x and y. The correlations [12] are obtained by acting on a single instance of the entangled state whereas the multiround approach uses in the order of states. Merging m instances together, we obtain the set of correlations[13]where , denotes the case when the remote state preparation succeeds and are the respective outputs. Thus, our Bell inequality may be written in the form [3]:[14]
Nonlinear Bell Inequality.
Here we derive a Bell inequality for the case where the parties have the option to abort at any stage of the protocol. Our inequality turns out to be nonlinear and will depend only on two parameters, and , defined as follows:
• —probability that Alice succeeded, i.e., her outcome is 1 (averaged over all observables by the measure μ):[15]This probability turns out to be equal to Bob successfully "guessing" the communication from Alice in the absence of communication from the latter.
• —conditional probability that Bob's outcome is equal to value of the function, given that Alice succeeded:[16]
Using roughly instances of the state , Alice obtains one successful outcome on average. Then, Alice communicates to Bob this successful instance.
To obtain the inequality, we show how Alice and Bob may guess the correct value of the function. In this setup, as in the previous case, Alice uses instances of the state . Then Alice communicates to Bob the first instance where the outcome appeared, using bits. Finally, Bob looks at the outcome for the successful instance and with probability obtains the value of the function f.
If Alice and Bob share a state that admits a local-realistic description, then the used communication cannot be smaller than the value , because it is the optimal value attainable by classical means. Thus, for any local-realistic state, we must necessarily have[17]See Supporting Information, section III for further details.
Examples show that our protocol produces large violations that are a bit weaker than the best known ones such as (16) or (9). This seems to be the price for its universality. However, it is an interesting open question, whether one can find a communication complexity protocol, such that the obtained Bell inequality would admit more dramatic violation than what is currently achievable. Another challenge is to decrease the amount of entanglement used to violate our Bell inequalities, which in our construction is exponential in the quantum communication complexity of the given problem. Similarly, the output size grows exponentially, which gives rise to the question of whether there exists a more efficient method of exhibiting the Bell nonlocality of quantum communication complexity schemes. The last two challenges could be addressed by devising a more efficient teleportation protocol or improving one of the existing ones (19). Finally, our method does not cover the protocols with initial entanglement. This is quite paradoxical, because protocols that use initial entanglement should be Bell nonlocal even more explicitly. It is therefore desirable to search for a method of demonstrating the Bell nonlocality of such protocols.
I) Proof of Lemma
Lemma 3.
For a protocol P supplemented by classical correlations and using bits of communication, the shifted success probability of computing f is bounded above as[S1]
Consider the success probability of the protocol P in the statement of Lemma 3 after the exchange of messages:[S2]To express the ratio [S1] we need to find in terms of communication complexity. We achieve this by using the amplification argument (see Supporting Information, section II for the proof), which boosts the success probability to 2/3 at the expense of sending at most bits of communication:[S3]Thus,[S4]
II) Communication Complexity for Arbitrary Success Probability from Communication Complexity for Fixed Success Probability
Here we use the amplification (pumping) argument, which is a well-known technique for increasing the success probability of a randomized protocol (20) by repetition, and prove the following bound for the communication required by a randomized algorithm,[S5]where stands for communication complexity of an arbitrary (quantum or classical) randomized protocol. The bound is valid for . We use the pumping argument to show that a smaller would enable one to construct a protocol that uses less communication than and achieves and hence leads to a contradiction.
Let protocol use bits of communication to achieve . Let us consider protocol in which Alice and Bob repeat protocol l times and then Bob returns as an answer the most common output of . Because we are restricted to Boolean functions, the success probability of is equal to the probability that protocol gives the correct answer no less than times. By the Chernoff bound we get[S6]Because we require that , we get that[S7]From the communication complexity bound, it is known that to achieve , the protocol requires at least bits of communication. On the other hand, protocol repeats protocol l times and uses bits of communication. Putting this together, we have[S8]Using relation [S7] we get finally[S9]For our estimation leads to a communication complexity bound of which is much below the true value. This discrepancy comes from the nonoptimality of the pumping protocol.
III) Rigorous Derivation of the Nonlinear Bell Inequality and Its Violation
We now derive the nonlinear Bell inequality[S10]where the classical communication complexity is additionally parameterized by μ and the size of the problem n. First, we construct a one-way protocol with classical communication that makes use of shared entanglement given the set of correlations. We restrict ourselves to the family of correlations with , . As usual, is interpreted as the success on Alice's side. When the latter occurs, we expect b to hold the value of the function . This restriction does not limit the generality because we may always take negation of , which is a local operation.
We show that for any correlation , characterized by n, , and (defined in the main text) leads to the protocol solving a problem of size n, using bits of communication and achieving for the initial probability distribution .
Protocol works as follows. Let Alice and Bob share copies of the correlations. They use their inputs x, y to select the appropriate measurements. Alice sends to Bob the index i of the first correlation where she obtained . Then, Bob estimates b for the respective correlation i and returns it as an output of protocol . In the case when none of the boxes returned , Alice outputs ABORT and Bob returns a random bit.
The protocol requires bits of communication to encode i of the box and 1 extra bit to encode the message ABORT. The probability that Alice gets for at least one instance is . For this case Bob returns with the probability . If Bob receives ABORT, he returns the proper value with probability . Putting we get an overall success probability of with communication of bits.
For all of the correlations with the local hidden variable model we get[S11]
In the case when the communication complexity is given only for the fixed probability of success , by the pumping argument and the fact that for we obtain[S12]
Using the fact that correlations obtained from a quantum protocol with communication complexity Q and success probability are characterized by and and inserting them into [S11], we make the following observation:
Observation 1.
Let be defined as in Eq. S10. If correlations obtained by construction of Eq. 2 in the main text from a quantum protocol with success probability and communication complexity Q do not violate the Bell inequality [S11], then[S13]
To witness the violation of a Bell inequality constructed for a particular function f, it suffices to know how dominates over for some fixed . [Function dominates if for any constant k there exists such that for any we have .]
IV) Memory Compression of Quantum Communication Protocols
We convert an arbitrary quantum communication protocol into one where on each round Alice and Bob compress their memory and teleport it alongside the message. This ensures that they do not store any information associated with the message between the rounds.
The theoretical underpinning of such conversion is Lemma 2, proved by Yao (3) and Kremer (14) (also ref. 21, lemma 7.2.1 and ref. 22, appendix A). Lemma 2 applies to protocols where only a single qubit is sent per round. One can also derive a version of the latter where the message size is variable per round, which gives a more efficient memoryless version of protocols that need only a small number of rounds.
Lemma 2.
The state of an -qubit protocol (without prior entanglement) on input can be written aswhere the and are complex numbers of magnitude , the are unit vectors belonging to Alice and Bob, respectively, and denotes the last bit of the -bit string i.
Consider the state description given by Lemma 2 for our quantum protocol after m rounds. Let describe Alice's local states encoded in k qubits, for some k. Because there are only different vectors , there exists a unitary and a collection of m-qubit states such that for all we have . [More precisely, we can find some orthonormal basis for the space spanned by the (not necessarily orthogonal) , which consists of at most basis vectors. Then we can write where T is the completion of the unitary transformation on the orthogonal complement of the subspace spanned by the vectors, to the orthogonal complement of the subspace spanned by the vectors.] Similarly on Bob's side there exists a unitary such that , where is the number of qubits used to encode Bob's local state in the original protocol and every is an m-qubit state.
Therefore, the state of the protocol after m rounds can be written aswhere and are the trivial local states on Alice and Bob, respectively. Then all of the local memory of the m-round protocol can be encoded in m qubits. This proves Proposition 1 in the main text.
Part of this work was done at the National Quantum Information Centre of Gdańsk as well as during the Program on Mathematical Challenges in Quantum Information, Isaac Newton Institute for Mathematical Sciences, 2013. This work is supported by European Commission (EC) IP QESSENCE, European Research Council (ERC) AdG QOLAPS, European Union (EU) project RAQUEL, Grant NCN Maestro (DEC- 2011/02/A/ST2/00305), the EU project SIQS, and MNiSW Grant IdP2011 000361. H.B. is partially funded through the Netherlands Organisation for Scientific Research Gravitation Grant Networks. S.S. acknowledges the support of Sidney Sussex College.
- ↵1To whom correspondence should be addressed. Email: ss870{at}cam.ac.uk.
Author contributions: H.B., Ł.C., A.G., M.H., P.H., M.M., F.S., and S.S. performed research; and S.S. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1507647113/-/DCSupplemental.
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- I) Proof of Lemma
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I think San Francisco is the best place in the whole world for an easy life.
- Imogen Cunningham
I don't love the world.
I think Jupiter should have hit us.
- Imogen Cunningham
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I was invited to photograph Hollywood.
They asked me what I would like to photograph.
I said, Ugly men.
- Imogen Cunningham
When I need names they drop out of my head;
when I don't need them they drop back.
- Imogen Cunningham
I hate big models.
- Imogen Cunningham
Oh, you ask me, what is the greatest torture of a person
who does portraits for a living? I could fill several
volumes with nice nasty stories.
I don't know.
- Imogen Cunningham
I don't know what love means.
- Imogen Cunningham
Well, I turn people into human beings by not making them into gods.
- Imogen Cunningham
A woman said to me when she first sat down,
You're photographing the wrong side of my face.
I said, Oh, is there one?
- Imogen Cunningham
I turn people into human beings by not making them into gods.
- Imogen Cunningham
When people ask me silly questions about my private life,
I just say, I don't discuss that.
- Imogen Cunningham
I was brought up on art.
My father thought I had a great hand at art and sent me to art school.
But he did not want me to become a photographer.
- Imogen Cunningham
It's silly to keep people alive who have a terrible disease.
- Imogen Cunningham
Some people say to me, Isn't it too bad that people
discovered you so late? I never thought that.
- Imogen Cunningham
When People magazine called me, I did the job on Ansel.
I'm older than Ansel and he has to mind me.
- Imogen Cunningham
Anybody is influenced by where and how he lives.
- Imogen Cunningham
When you do portraits professionally it's not a desire,
it's for money.
- Imogen Cunningham
I was poor.
When you're poor you work, and when you're rich you
expect somebody to hand it to you.
So I think being reasonably poor is very good for people.
- Imogen Cunningham
Get it out of your historic head.
- Imogen Cunningham
There are certain things you don't discuss with Ansel,
especially if you don't agree.
- Imogen Cunningham
I don't talk about success.
I don't know what it is.
Wait until I'm dead.
- Imogen Cunningham
I became kind of a drop-out in science after I came back to America.
I wanted to photograph.
- Imogen Cunningham
I'd never kill myself for a man.
I wouldn't do it for anybody.
- Imogen Cunningham
I told the students that whatever they did in class was for the wastebasket.
- Imogen Cunningham
I don't think there's any such thing as teaching people photography,
other than influencing them a little.
People have to be their own learners.
They have to have a certain talent.
- Imogen Cunningham
Laugh when you can,
apologize when you should,
and let go of what you can't change.
Life's too short to be anything... but happy.
- Anonymous
If you don't know where you're going,
any road will take you there.
- Lewis Carroll
(Alice in Wonderland)
To go against the dominant thinking of your friends,
of most of the people you see every day,
is perhaps the most difficult act of heroism you can perform.
- Theodore H. White
Footprints in the sands of time...
Where have you been?
Where are you going?
Why are you going there?
- Jonathan Lockwood Huie
The greatest mistake you can make in life
is to be continually fearing you will make one.
- Elbert Hubbard
The true meaning of life is to plant trees,
under whose shade you do not expect to sit.
- Nelson Henderson
Whatever you do, do with kindness.
Whatever you say, say with kindness.
Wherever you go, radiate kindness.
- Jonathan Lockwood Huie
You're only here for a short visit.
Don't hurry. Don't worry.
And be sure to smell the flowers along the way.
- Walter Hagen
The way I see it, if you want the rainbow,
you gotta put up with the rain.
- Dolly Parton
You don't have the power to make life "fair,"
but you do have the power to make life joyful.
- Jonathan Lockwood Huie
Change what you see,
by changing how you see.
- Jonathan Lockwood Huie
Believe nothing, no matter where you read it,
or who said it, no matter if I have said it,
unless it agrees with your own reason
and your own common sense.
- The Buddha
Nobody can bring you peace but yourself.
- Ralph Waldo Emerson
You are never too old to set another goal
or to dream a new dream.
- C. S. Lewis
You will not be punished for your anger,
you will be punished by your anger.
- The Buddha
A well-developed sense of humor
is the pole that adds balance to your steps,
as you walk the tightrope of life.
- William Arthur Ward
The cave you fear to enter holds the treasure you seek.
- Joseph Campbell
Powerful Dreams Inspire Powerful Action.
When you can taste, smell, and touch your dreams,
you can enroll the world.
- Jonathan Lockwood Huie
Choose the World You See,
and See the World You Choose.
- Jonathan Lockwood Huie
Don't Take Anything Personally.
Nothing others do is because of you.
- Miguel Angel Ruiz (don Miguel Ruiz)
Simply do your best, and you will avoid
self-judgment, self-abuse and regret.
- don Miguel Ruiz
Holding on to anger is like grasping a hot coal
with the intent of throwing it at someone else;
you are the one who gets burned.
- The Buddha
Faith is taking the first step,
even when you don't see the whole staircase.
- Martin Luther King, Jr.
People will forget what you said,
people will forget what you did,
but people will never forget
how you made them feel.
- Maya Angelou
How do you want to be remembered?
Live life full out - Begin today.
- Jonathan Lockwood Huie
May the world be kind to you,
and may your own thoughts be gentle upon yourself.
- Jonathan Lockwood Huie
Life is as easy or as hard as you think it is.
- Jonathan Lockwood Huie
If you aren't in the moment,
you are either looking forward to uncertainty,
or back to pain and regret.
- Jim Carrey
Life is without meaning.
You bring the meaning to it.
The meaning of life is
whatever you ascribe it to be.
Being alive is the meaning.
- Joseph Campbell
Twenty years from now you will be more disappointed
by the things you didn't do than by the ones you did do.
So throw off the bowlines.
Sail away from the safe harbor.
Catch the trade winds in your sails.
Explore. Dream. Discover.
- widely misattributed to Mark Twain
Whatever you do, you need courage.
Whatever course you decide upon,
there is always someone to tell you
that you are wrong.
There are always difficulties arising
that tempt you to believe your critics are right.
- Ralph Waldo Emerson
If the only prayer you said in your whole life was,
Thank you, that would suffice.
- Meister Eckhart
Take time to play!
Ask for what you want.
Live loudly.
Be avid.
Learn a new thing.
Be Yourself!
- Mary Anne Radmacher
May flowers always line your path and sunshine light your day.
May songbirds serenade you every step along the way.
May a rainbow run beside you in a sky that's always blue.
And may happiness fill your heart each day your whole life through.
- Irish Blessing
To laugh often and much;
to win the respect of intelligent people
and the affection of children,
to leave the world a better place,
to know even one life has breathed easier
because you have lived,
this is to have succeeded.
- Ralph Waldo Emerson
Live with intention.
Walk to the edge.
Listen hard.
Practice wellness.
Play with abandon.
Choose with no regret.
Appreciate your friends.
Continue to learn.
Do what you love.
Live as if this is all there is.
- Mary Anne Radmacher
It is the friends you can call up at 4 A.M. that matter.
- Marlene Dietrich
A friend is someone who knows all about you,
and loves you just the same.
- Elbert Hubbard
A true friend is someone who
thinks that you are a good egg
even though he knows that
you are slightly cracked.
- Bernard Meltzer
May your life always be Counterpoint to the Clamor of the World.
May you delight in Dancing Lightly With Life.
May you soar on eagle wings, high above the madness of the world.
May you always sing Melody in the Symphony of Your Life.
May you taste, smell, and touch your dreams of a beautiful tomorrow.
May your sun always shine, and your sky be forever blue.
- Jonathan Lockwood Huie
Be thankful for what you have; you'll end up having more.
If you concentrate on what you don't have,
you will never, ever have enough.
- Oprah Winfrey
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subset: commoncrawl


text:
ID code: JHGMOEDP34
Midnight Oud Perfume by Juliette Has a Gun. Midnight Oud came out from the Stable of Juliette Has a Gun in 2009. The perfume presents an arresting combination of romance and rock, steel and roses, velvet and swords that makes life so unpredictable and interesting. Make your way through the highs and lows of life with style, making and leaving memories of your unique personality, capture life in your palm and do things just your way with confidence and elegance. This fragrance with all its richness is yet so subtle with the enigmatic oud lacing its texture. An array of notes compose this fragrance with accords of moroccan rose, oud, amber, several sorts of musk, saffron, geranium and patchouli oil. All products are original, authentic name brands.
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Henri Verstijnen
Evening Ydille
"Avond Ydille" or "Evening Ydille " a lithograph on thick paper by Henri Verstijnen. It is signed in the print in the right bottom. The lovely artwork measures 17×13 cm and has been washed to preserve and clean the artwork. It is now in good condition and ready for years to come. This lithograph was made between 1920 and 1930. It is shipped as a loose sheet on a acid-free backboard and a paper cover so you can store or frame the artwork as you see fit.
Price: 55 euro (exclusive additional shipping costs)
Click on the images for a larger view of the artwork.
Click here if you want read more about Henri Verstijnen or if you wish to see other works by Henri Verstijnen that are for sale in Jo Hulsteins shop.
If you are interested in purchasing this work or if you have additional questions, please use the form below.


text:
Equilibrium constants, such as the dissociation constant (of protein-DNA interactions using
Equilibrium constants, such as the dissociation constant (of protein-DNA interactions using the FA method. needed. The of the IgE-aptamer pair was determined as 6 2 nM which is consistent with the reported results (8 nM). determination using FA In the IgE-aptamer pair, aptamer is the binding ligand, and IgE proteins may be the binding focus on. IgE-aptamer complicated dissociates based on the pursuing formula. represents protein-aptamer complicated, and so are the proteins as well as the tagged aptamer, respectively. The dissociation continuous of complex can be expressed in Formula 2 and [can be determined by Formula 4 [26]. depends upon the ratio could be determined by both plateau heights from the free of charge (from the free of charge and destined aptamers was acquired by Formula 5, where was the free of charge aptamer plateau height obtained at E1, and was the bound aptamer plateau obtained at E2. The plateau height was the average of 3 injections. Table 1 shows the values determined at different aptamer concentrations in the incubation buffer while the IgE concentration was kept constant (20.0 nM). As can be seen, the obtained is independent of the aptamer concentrations used, and the average value is 6 2 nM, which is consistent with the reported results of 8 nM [29] and 9 nM [30]. Figure 4 Two sets of plateaus obtained at two voltage configurations. The sample solution consisted of 20 nM IgE and 70 nM aptamer. The set of c1 and a1 was obtained with the voltage setup in Figure 1c. The other set of c2 and a2 was obtained with the voltage … Table 1 Determined Kda) at different aptamer concentrations 4 Concluding remarks Microchip CE is a powerful tool for binding studies of protein-DNA systems. The short detection length (1.0 cm) used here reduced the analysis time and might reduce protein loss due to adsorption on the channel walls during separation. FA is an accurate and dependable method to determine the dissociation constants of some slow-off binding systems. LIF detection used in FA is advantageous for high sensitivity and no inner 40013-87-4 IC50 standard requirement. Even though the migration speed dependence of fluorescence emission triggered some difficulty in tests primarily, this impact was conveniently altered by establishing a compensating voltage settings based on the comparative migration velocities from the free of charge and destined aptamers. To lessen possible error because of fluctuations of fluorescence emission as time passes, multiple shots and separations can be executed for both voltage configurations alternatively. One surely may use an internal regular for the binding tests as well as the empty aptamer (without IgE added) to look for the bound aptamer proportion, however the best CFD1 internal standard continues to be hard to select for FA often. In FA, treatment must be taken up to 40013-87-4 IC50 insure the parting buffer as well as the test buffer possess the same conductivities in order to avoid the test stacking effect. The same test and parting buffers are utilized generally, but their conductivities may still possess just a little difference when the test solution includes some proteins and aptamers which most likely raise the viscosity from the test solution and reduce its conductivity. Furthermore, stacking might occur because of ionic transport amount mismatch on the boundary from the test plug as well as the parting buffer [31]. Both effects could be negligible when low concentrations of aptamers and proteins are used. The fluorescence linearity with concentration may be another concern. Therefore, the destined and free of charge aptamers should generate plateaus with equivalent levels, which may be controlled by choosing the approximate original 40013-87-4 IC50 concentrations of aptamers and proteins. Finally, it ought to be observed that the technique developed right here may only end up being helpful for slow-off binding systems with < 10 nM. Acknowledgements We enjoy Professor Carl J. Seliskar and Aigars 40013-87-4 IC50 Piruska (Department of Chemistry, University of Cincinnati) for a discussion of photobleaching phenomenon. This project was supported by NIH with grant number GM 69547. Abbreviations CEcapillary electrophoresisFAfrontal analysisLIFlaser-induced fluorescenceTGKTris/Glycine/K2HPO4BRbuffer reservoirSRsample reservoirBWbuffer waste reservoirSWsample waste reservoir Notes This paper was supported by the following grant(s): National 40013-87-4 IC50 Institute of General Medical Sciences : NIGMS R01 GM069547 || GM..
This scholarly study investigated the microbial degree of Streptococcus mutans and This study describes the direct detection of the biological toxin (Ricin)
Equilibrium constants, such as the dissociation constant (of protein-DNA interactions using
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About Lowther7, LLC
Take that leap in 2018?
How long have you been putting off the development of a strategic education plan? Do you still need to complete the needs assessment of your key constituents? Are you weighing how much time you can pull from your regular projects to cover the organizations education activities? Are you concerned about the ongoing quality of your education programs? Not sure what your technology delivering options are?
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The team leaders of Lowther7 have collaborated on projects together for over 25 years. Their combined experience covers a variety of projects and educational models, providing learning solutions for professional and trade associations, non-profits, design firms, and corporations.
Thom Lowther, Ed.S.
Washington, DC
Thom has worked with professional and trade associations; with private sector firms; A/E/C product manufacturers; and several government agencies - as both an employee and external consultant; and as an administrator in higher education and later as an adjunct professor. He is an expert in finding the right learning solutions for the organization. He has assisted organizations to reach new audiences and to establish or enhance their professional education programs. Thom has taught a variety of workshops and online courses related to leadership, marketing, future trends, organizational behavior, and professional development. He is a former Jury member for the LearningElite Awards and contributing author to the PSMJ Resources monthly newsletter. He shares his knowledge as a coach, speaker, author and blogger.
Katin Imes
Chief Technology Officer (CTO)
Expedition 21 Media.com
Eugene, OR
In addition to currently managing more than 40 websites for performance, security, and SEO for both clients and dev-ops projects on cloud servers, local servers, and hosted servers, Katin designs and implements our instructional mini-games for online courses. Mini-games create strong engagement, enhanced understanding and exploration of new information and application, and can serve as demonstrations of competency. Here is a free, NEW mini-game -demonstrated at GREENBUILD 2014 - that appears in a course after students have learned how to qualify building materials for the new LEED Materials Reporting credit:
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• Software engineer: 20+ years
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• Web Developer: 20+ years
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• Game Developer: 15+ years
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• Big Data analysis and systems: 5+ years
• Website performance, security, and SEO: 10+ years
Lowther7 is a Veteran owned business


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There are some traders who take their execution times so seriously that they are willing to pay up huge sums of money to their brokers for the best times. Stock quote for The Charles Schwab Corporation SCHW - Get real-time last sale and extended hours stock prices, the content of the site including but not limited to material, Salt-Upon-Wounds. Memilih Unsur Seni Rupa untuk Dikembangkan Menjadi Karya Seni Rupa.
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Summer finds several of us limp, enervated, and exhausted. Rising temperatures put us in misery. These are symptoms of reduced water levels in the body. To enable us to run through our day effectively, we need to keep a close watch on our hydration levels. We can live without food for much longer than living without water. The importance of this simple nutrient is often underestimated.
So why is water important for us? What does water do to our body? Did you know that 70% of our body is made of water?
Among other functions, water is extremely necessary for these -
- Water helps to circulate blood and other nutrients around inside the body.
- Water removes toxins and waste from the body in the form of sweat, urine and stools.
- Maintains body temperature by removing heat from the internal organs, and flushing it out of the body through sweat.
A decrease in water leads to several disturbances in normal body functions. Absence of enough water in the body leads to a condition called dehydration. How do we recognise these symptoms?
- Do you know that your trips to the washroom are the best indicator of hydration levels? If you have yellow urine, accompanied some times with a burning sensation while urinating, OR if you have visited the washroom lesser than 2 times in the last 5 hours, and have been exercising or playing outdoors as well, then it is urgent that you sip up on fluids. Colourless urine is the best sign of hydration.
- Thirst – you have already lost 1% body water by the time the brain signals thirst! If you have not heeded your thirst signals, and are still away from your water bottle, you could experience some of these too -
- Dry around lips, fuzzy tongue.
- Increase in body temperature.
- Giddiness, shortness of breath.
- Confusion, lack of muscular coordination, muscle cramps.
- Loss of control over bowel movement!
- Beware! A bad combination of excessively hot weather, loss of body fluids and not enough water replenishment can lead to heat stroke and even death.
How many of us really want to get to such extremes? We can quickly reverse these symptoms by drinking up. At the first sign of dehydration, or even before that, start drinking up. How much water should we drink? The National Institute of Nutrition recommends at least 8 glasses of water daily for an average Indian. In summer, during exercise or when there is excess sweating, the recommendations go up higher.
Featured in picture - Tintrinee Panaka – Refreshing Tamarind Drink. Good way to hydrate in scorching heat.
The best way to re-hydrate is by sipping small mouthfuls of water throughout the day. Much like drip-irrigation in a field. Set up a pretty 1 litre glass bottle with drinking water close to your work station. Down a gulp every 10 minutes. This way, your water will last you for about 20 mouthfuls. If that is difficult, at least drink half a cup of water or other fluids every half an hour. This is more effective than drinking larger volumes at one time and going without fluids for long stretches of time.
Are there any other fluids that we can sip on? Surely, some people get nauseated from gulping only water throughout the day. Yes, there are some really healthy fluids that help you hydrate. Fluids like barley water, tender coconut water, diluted buttermilk, skim milk, unsweetened lemon juice, unsweetened fresh fruit juice, raw unsweetened juiced vegetables, and are all great for keeping our body in safe hydrated zones. All these fluids also bring some vital nutrients like vitamins and minerals apart from replacing fluid losses in the body.
Featured in picture - Aloe vera Lemonade – with the cooling properties of Aloe vera.
Then there are some foods that are high in moisture too. They help the body by adding valuable nutrients that are lost in excessive sweating. Foods that include moisture and essential minerals are cucumber, tomatoes, raw bottle gourd, watermelon, cantaloupe, oranges, apples. These are best eaten raw to ensure all the nutrients plus the water reaches the body.
In the next post, I will be discussing what fluids are not good for hydration. Also whether children, elderly, pregnant or sports people need any special hydration in summer.
Do write in if you have any unique dietary concerns for yourself or your family.


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We took a littel roadtrip this weekend and visited Tom & Anj's folks in Durango, CO. It's about a 5-6 hour drive each way. We had a great time and saw some amazing sights. I was suprised not to see any snow however. Ah well. We are back in Denver and Adam is at work right now. Our new couches got delivered (finally!) this morning.
I'm attaching some pictures for your enjoyment. 🙂
These are the Mesa Verde cliff dwellings. They are about an hour outside of Durango.
Tom took us to Baker's Bridge where people jump off. There was a guy fishing under it so the boys decided to jump off a huge cliff instead. The water was FREEZING! (Mountain runoff)
Anyone who has seen "Beerfest" will appreciate the drinking of "das boot"!!!
A fun new shot of the Prices at Mesa Verde.


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|Isabel de Beaumont
(Cir 1102-Cir 1172)
Isabel de Beaumont
Isabel married Gilbert de Clare Earl of Pembroke (1st). (Gilbert de Clare Earl of Pembroke (1st) was born in 1100 in Tonbridge, Kent, England and died circa 1147.)
Please add your comments to the
Table of Contents | Surnames | Name List
This Web Site was Created 5 Sep 2013 with Legacy 7.5 from Millennia


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Oh st Jude, apostle of my saviour, intercede for me in this time of trials that i may receive a miracle of academic sucess in my results yet to be released. And for the hope and strength to work hard and avoid any circumstances that will prevent me from attaining academic excellence. In Jesus name i pray.
Return to A Prayer for Hope


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Summer Garden Picnic
Summer Garden Picnic
Flagstaff, AZ
Join the Flagstaff Family Food Center for our first annual Summer Garden Picnic Fundraiser, sponsored by the Northern Arizona Association of Realtors. Ticket sales are limited and will sell out, buy yours today! Ticket price includes dinner, open bar and a private screening of the award-winning ...
Saturday, August 26 2017 5:00 PM — 9:00 PM


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An unusual case of a patient presenting with left sided pulsatile tinnitus is presented. This was later shown to be due to a dural arteriovenous malformation involving the lateral venous sinus. The diagnosis was suspected by the presence of a bruit over the mastoid process and confirmed by a CT scan and angiography. Management involved pre-operative embolisation and neurosurgical excision. The differential diagnosis of pulsatile tinnitus and the management of a dural arterio venous malformation is discussed.
Email your librarian or administrator to recommend adding this journal to your organisation's collection.


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This month, Arlington, MA community members of all ages participated in a multi-day Whimsical Weavings program at Brackett Elementary School and at the Robbins Library. They discovered how to make colorful, playful weavings utilizing discarded, reusable, recyclable, and natural materials. First, they learned about how textiles have developed and reflected societies throughout the world. Then, they created these personal textile artworks and larger-scale collaborative piece from old garments and biodegradable fibers such as cotton, wool, silk, and jute fibers.
Turtles, beavers, and herons, oh my! In this 8-class program, Project Connection 3rd & 4th graders at Muddy Brook Elementary in Great Barrington, MA learned about the creatures and plants that live in their local pond ecosystems and the critical role these wetlands play in environmental health. They discovered ways to be eco-friendly artists, making their projects from materials such as discarded magazines, newspapers, tissue papers, cardboard, milk paint, natural watercolors, and homemade glue. When dismantled, the materials in the installation will be recycled, composted, or up-cycled for a new project in effort to have zero waste.
Earth Prints all around! This month, we had a great time facilitating this print/mark making workshop for kids and adults on both coasts at California Academy of Sciences, Pickleweed Library in San Rafael, CA, and at the Lucius Beebe Memorial Library in Wakefield, MA. Experimenting with homemade spice and veggie watercolors, mica paints, brushes made from nature, wax, and more, the resulting prints were absolutely beautiful and very unique!
It was a quite a musical summer for us! Among our programs, we facilitated our Upcycled Instruments and Musical Mobiles workshops at lots of libraries on both coasts. Their very fun 2018 Summer Program theme was Libraries Rock! - a perfect fit! Children and adults made wonderful acoustic artworks using utensils, tape roll cores, fallen birch branches, tissue boxes, miscut keys, and more! What fun it was to hear each sound add to the collective as the participants finished their projects o one-by-one. Also, thank you Tricorner News for this great article of our program at Scoville Memorial Library in Salisbury, CT.
We were delighted to work in partnership with The Exploratorium in San Francisco during their Inflatable exhibit this summer! In July, museum-goers reimagined cork, pins, drink tabs and other odds & ends into a fantastic array of Itsy Bitsy Beings in July. Then, in August we returned to create glowing sculptures with kids and their families during our Light Impressions workshop. We had a blast working with over 200 participants!
We celebrated Earth Day 2018 early at the Pine Plains Public Library this past Saturday! Participants in our Multigenerational Eco-Jewelry workshop made wonderfully whimsical earrings, necklaces, and key chains. For their one-of-a-kind pieces, we incorporated de-shelved library books (such as song books, field guides, and encyclopedias!) as well as a variety of items collected from nature. Thank you to all the enthusiastic participants who joined us to experiment with up-cycling materials!
Thank you to all the Brackett Elemenary After School crew who participated in our 2-session bookmaking workshop! Each teacher/artist made personal collage books inspired by their personal histories using discarded books, magazines, catalogue pages, calendars, and more! They explored what home means to them, both past and present, and shared these ideas through the creation of a self-portrait collage book (and some really great haikus!) These were then displayed for their parent-teacher Spring Fling. It was so much fun to learn about everyone and see how each individual visually represented themselves!
We just wrapped up our winter series of workshops at Brackett Elementary School. It was so much fun to return for our 2nd year to work with the K-5 students and staff in the after school program. In our time together, we made glowing Winter Wonder-lanterns and handcrafted many dozens of cards and envelopes in our Valentines - The Green Way! program. Participants learned about the environmental impact on the production of new glass and paper, recycling, and various ways that we can be earth friendly in making art. We look forward to returning in March to do more eco-art projects with this fantastic group!
It was wonderful to be back at Lincoln High School, working with Green Academy students for our fifth year running! This year, 10th and 12th graders participated in our Small Worlds workshop. They reflected on memories and significant places in their lives. They depicted these ideas using found images in magazines, postcards, old photographs and created 3D collages inside small boxes. Special thanks to our TA's Haya and Gianna.
"The workshop was very fun. I enjoyed working with all the materials. I would recommend this to to others. Thank you for a wonderful art class." - Workshop Participant
This weekend, we had the privilege of facilitating our Winter Wonder-landscape workshop at Memorial Hall Library in Andover, MA. It was wonderful to see the enthusiasm of children creating art with grandparents, and daughters alongside their parents. Participants made beautiful accordion books of snow-filled mountain landscapes, polar animal habitats, and more!
This December, we participated in the Tis The Season For Science event at the California Academy of Sciences in San Francisco. At our tables, museum goers had the opportunity to express their ideas of very cold and far away landscapes. Inside tiny boxes they incorporated their imagery in mini-dioramas and crafted an environment for their chosen Arctic or Antarctic animal. The event atmosphere was complete with falling snow in the museum atrium!
"What a great workshop! Our Girl Scouts had an absolute blast and me too! Love the craft itself and the concept of green art was well." - Parent/Troop Leader
With perfect timing, our first snowfall of the season arrived on the morning our our girl scout workshop. Inspired by the weather, daisies and brownies from troops in Northeastern MA joined us to make Winter Wonder-lanterns. First, they learned about the life-cycles of glass and paper and then creatively upcycled jars, deshelved library books, magazines, junk mail envelopes, and tissue paper into beautiful light-filled artworks.
This Fall, Paul Revere School 3rd & 4th graders participated in a Paper Palate residency program. They learned about the life-cycle of paper, food sustainability, and culture by creating a paper food Japanese restaurant. On the final day of the program the students celebrated their creative work by serving their colorful paper bento boxes, sushi and tea to their peers.
"Always looking for ways to recycle! This is great, creative, fun, useful. I can never say I don't have a card when I can make one! Thank you!" -Art Cards Participant @ Falmouth Library
This summer, we enjoyed facilitating numerous workshops at libraries throughout the Bay State, including programs in Falmouth, Kingston, Acushnet, Reading, and Andover, to name a few! Among our programs, we had a wonderful group of participants make Art Cards - The Green Way at Falmouth Library using de-shelved books, magazines, maps, and discarded mail. Also, at our family-friendly workshop at Acushnet, kids and their parents made all sorts of cute, creepy, and humorous Itsy Bitsy Beings. The creativity that went into these 3D assemblage pieces from paper and metal scraps was very impressive!
This winter, each class at Glen Park Elementary School participated in a special Pop-Up Habitat program focused on the neighborhood ecosystem of Glen Park Canyon! The k-5 students created their own wearable art and became the creatures that inhabit this landscape using improv and other drama techniques. It is very exciting to see this program culminate through both visual and dramatic self-expression.
In this 5-week Green Art Workshop series, BASP kindergarten-5th graders became eco-conscious artists. Utilizing everyday discarded materials, they first experimented with drawing and collaging patterns from their imaginations and from observations of the school environment. Next, participants learned to make handmade paper from flyers, egg cartons, old paper, and junk mail. Finally, students brought these elements together to design unique quilt blocks. These individual "green" artworks now form the giant collaborative paper quilt that is displayed in the school library.
Students from Willie Brown Middle School had the opportunity to engage in SCRAP in a rather unconventional way during the Community Cartographers workshop! During their field trips, they led each other on blindfolded tours and created sensory maps of their journeys, focusing on their sense of touch and sound. The middle schoolers also explored the artistic potential of mapping further by up-cycling old maps, using collage and embroidery techniques to depict a personal story.
This May, we returned to Bryant Elementary and worked with each class to create a collaborative paper quilt installed at in their School. The students learned about the African American quilting tradition of Gee's Bend, Alabama. Inspired by the Gee's Bend quilts and images of San Francisco, the participants designed their own quilt blocks using various colors of paper scraps.
This spring, we facilitated Fresh StART, our teacher training program, with teens at Balboa High School. In March and April, the students met with GAW teaching artists to do a variety of green art projects such as Dreamscape Books, Mapping Personal Journeys, Cork Abstractions, and Ephemeral Nature Sculptures. (Thank you Patti Pauchnick, Laura Boles Faw, and Miles Epstein!) Inspired by the artists, hands-on making, and a visit to SCRAP, the teens then designed their own green art lesson. The program concluded with students teaching their unique creative re-use projects to their peers at Balboa.


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Spring School Program 2010
This post is also available in: Japanese
|Spring School 2010
| Pamphlet in PDF
Please click on the icon to view/print
|Vibrant Spring!
|The children will learn about the life of a butterfly, enjoy mixing colors and create a "Garden of Colors".
They will have fun singing, dancing, reading, writing, drawing, painting and going on a picnic.
| Tue, 23rd – Fri, 26th of March
9:30 AM to 2:00 PM
|Eligible Age
|2 years to 12 years old
|Note: Children aged 4-6 years old are eligible provided they speak & understand English.
|All classes are separated by age grouping.
| The Spring course costs 20,000 yen + Material fees cost 9,000 yen.
(The lunch cost is included in all the above and will be catered by the Musashino Food Center)
NB: Snacks are provided free of cost at 10:30 AM
|Application deadline
|Until Thursday, the 18th of March
|Application forms
|Please read the terms and conditions then download the document file, select the appropriate entries, enter information, save, print, sign and fax it along with a copy of payment receipt to 0422-57-8306.
|To Reserve
|Little Angels International School
4-9-15, Honcho, Kichijoji, Musashino-shi, Tokyo 180-0004
Tel: 0422-57-6887
Fax: 0422-57-8306
This post is also available in: Japanese


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Welcome Home!
"We'll Make Your Move A Reality!"
CARMICHAELS BEST KEPT SECRET! Located off Madison and Manzanita, our community is within walking distance to shopping and restaurants.We offer two bedroom one bath homes and one bedroom Cottage style apartments that feature spacious country kitchens with modern appliances. Large walk-in closets and spacious patios offer room for your growing family.


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Price Inspector UK - Find the Best Deal
PriceInspector Suggestions
We have displayed the biggest prices in the UK for aging anti treatment in Skincare and Pampering including these related brands: PRIMO HERB, PRIM AND PAMPERED, SKIN IMAGE, ALTERNA, OLAY.
To narrow your aging anti treatment search you can use the list of Refined Categories on the right or further drill down by using PriceInspector's search bar at the top. Either way, you should find the best deal on your new Skincare items on this page.
Refine by Category


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Article archive
First blog
Our new blog has been launched today. Stay focused on it and we will try to keep you informed. You can read new posts on this blog via the RSS feed.
Website launched
Our new website has been launched today. Tell your visitors why you have started a new presentation and how it benefits them. Mention your goals and project advantages.
Items: 1 - 3 of 3


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Puzzle BobbleSuper Famicom Japanese (NTSC-J) Games
BEST DEAL(poor label) - $4.99
The classic game Puzzle Bobble (AKA Bust-A-Move in the US) has arrived on your SNES with all the addictiveness one could want (or not want, depending). Match the colored balls to pop them and clear the board. How far can you get?
NOTE: All photos depict good condition items only; actual product may vary.
Product Details
Product Variations
Not a member? Register for free!


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While browsing some blog posts this morning I came across a very interesting idea that Kathy Cassidy has for students to practice reading smoothly (reading fluency) and record and learn from listening to themselves read using Vocaroo. Students can hear if they are reading fluently or not and compare it to what fluent reading should sound like. I think this allows students to take a bit of responsibility of their own learning and be able to identify their own growth.
The program that she used to help her grade one's improve their communication skills is Vocaroo (she found out about it via Twitter…surprise surprise)
"Vocaroo's website says, "Vocaroo is a shiny new service for sending voice messages across the interwebs." It allows you to record your voice, play it back to listen, and then provides you with a url or the html to embed an icon into a webpage or blog."
After experimenting with it myself, I found out that this tool is extremely quick and easy to use. I decided to read a nursery rhyme while recording my reading on Vocaroo to see if I read smoothly or not.
I could see myself using this tool in a variety of ways as well; I think that since it is so easy to use, you could use it as a center for students to practice their reading independently and for you to listen to it later on to assess their communication skills. Since there were not any complicated steps to it, Vocaroo is easily linked to your class blog for parents to listen to as well. Students can be proud of their progress and it can be heard by using this tool throughout the school year.
The only con I found with it, besides the fact that it won't upload directly onto my blog, was that if a student makes a mistake with his/her reading, he/she cannot edit the recording and has to begin recording again from the very beginning. Despite the one very small con, this tool will definitely be on my list of things to try with my class next year.


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Dear friends,
I can finally announce our group-exhibition in Makurazaki, called "Wind from Europe".
Different artists from Holland, Belgium and Germany will show their works in the Nanmeikan Museum of Makurazaki from Aug.20st-Sept. 19th.
I will come to the opening and hopefull also September 16&17.
Here is a the list of all the artists:
Please take a look at their websites to see their works:
Nagae Kinuko, Japan: http://kinuko.jp/
celebrating 20 years of her beautiful Hindeloopen-art
Els van Baarle, Holland: http://www.elsvanbaarle.com/
She is coming toward the end of exhibition.
Helene De Ridder, Belgium: http://www.helenebatik.be/
Jacques Coenye, Belgium: http://www.jacquescoenye.be/
Ria van Dijk, Holland: http://www.riavandijk.nl/
Rita Trefois, Belgium: http://users.telenet.be/ritatrefois-batikart.be/
Erika Fiedler, Germany... a wonderful friend of mine,
who has already exhibited in Japan several times.
She will also have an exhibition of scarves in Makurazaki from Sept 13st- Sept 18st
and Julia Takagi (me)
and Julia Takagi (me)
Here are my works, which will be displayed and also available during the show.
Looking forward to see you at the opening !!!


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One week from today: PVCA is participating in Centre Gives , a time when you can maximize your donation to PVCA with a (prorated) match from the Centre Foundation May 6th & 7th -- a 36 hour window. Visit our website during this time to participate with a community of people around the nation sharing in abundance.
At PVCA we are working to create abundance in our communities in collaborations, science and the arts.Here are a few words from PVCA Member Jennifer Tucker on why she supports PVCA-
<iframe width="560" height="315" src="//www.youtube.com/embed/Y0vK9Lxan6w" frameborder="0" allowfullscreen></iframe>
We could not do what we do without your support.
May 6th is the time to do it. Your financial support will help to implement restoration and education projects throughout the Upper Penns Creek Watershed.
Thanks for reading


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Information on this page is provided for information purposes only. The Portsmouth Catholic Diocese is not responsible for its accuracy.
Although our main work is educational and political (we have spearheaded every attempt to change the law in Parliament), we have raised funds for research into abnormalities in childbirth and give assistance to expectant mothers in need. We have as members people belonging to all religious denominations and none. We all share a respect for the sanctity of human life, no matter how small, and we are determined to see an end to the holocaust which has resulted from the 1967 Abortion Act. There are
|Area Contact
|Mr R Allen (Basingstoke group)


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TDDO: Ridonculous Race!
TDRRDO is here! Check out the premiere on dA!
Pahkitew Do Over
Total Drama Pahkitew Island Do Over has officially ended! Congrats to the winners!
Revenge Do Over
Total Drama Revenge Do Over has been a blast! Thank the OC creators!
Please keep all material on site TDDO related, please. In chat, you may go wild.
News and events
- The wiki is in the process of being updated. Make sure to be careful! There are spoilers here! Once you've read TDIDO, TDADO, TDWTDO, TDASDO, TDRDO, TDPDO, and the upcoming TOTAL DRAMA: RIDONCULOUS RACE Do-Over, you can fully feel free to roam every corner of this site! You're also encouraged to update and edit as you please!
- We now have a chatroom on Chatzy which is free for roleplays and fun all around! Speak to the TDRDO OC winners and the writer of TDDO! No account required. Free access!
- >>>> http://www.chatzy.com/73588258037924<<<<<
- There is also a TV-Tropes Page which anyone can edit! (It's really lacking in content, and the only requirement to add to it is to have read the fanfic. Go nuts, tropers.
- Total Drama Pahkitew Do Over is done! Feel free to update any information on this wiki as long as it corresponds to the events of the fanfic itself.
- This wiki gives A LOT of credit to TDWiki. Pretty much everything about this wiki is based on their setup and design. CREDIT to the coders, admins, and designers there for being so inspirational.
© The TDDO Series is a fan work that is inspired by and centered around the characters/settings/premise/etc. from the reality show spoof series, "Total Drama" that belongs to Teletoon Studios, Fresh TV, Cake Entertainment, and its creators, Jennifer Pertsch and Tom McGillis.
Click this link to learn about the character OC's and then read the actual fanfic. Enjoy.
About Total Drama Do Over
Total Drama Do Over started on September 28, 2012. It CAN'T be posted on Fanfiction.net because it's in script format, where everything is laid out as if it was a movie script. It's all on deviantArt.com.
This was on "purpose" because, as a visual learner, CoGreen knows it's tough to pay attention when everything is cluttered into paragraphs. He believed this way would help him get work done faster, and keep people from getting disinterested as the updates would not take too long. He's also incredibly lazy.
New episodes come out every Sunday, the moment Sunday starts. Midnight.
The TDRRDO release date will be released after the last 'Get Don'c' team reveal. The release date has a release date. Weird.
He, MightyMewtron, and Christlover357 hope you enjoy. TDRRDO consist of an entirely new writing team along with CoGreen2.0. Lolitafreak88, Mysterion305, Clyde-The-Snivy, GyroMaster, TDIFANMIKE, and TrixieLulaMoon323
Seasons of Total Drama Do-Over
Total Drama Do-Over Wiki is about the fanfic created by CoGreen2.0. Total Drama Do-Over is a fanfic about Total Drama Island, if everyone had competed in Season 1. All of the characters. So read, enjoy, and have fun.
|TDDO Season One
|TDDO Season Two
|TDDO Season Three
|TDDO Season Four
|TDDO Season Five
|TDDO Season Six
|TDDO Season Seven


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20121214 postfix-2.9.5にupdateしました
Release notes
Release notes
Postfix stable release 2.9.5, and legacy releases 2.8.13, 2.7.12, 2.6.18 are available. They contain fixes and workarounds that are also part of Postfix 2.10. Postfix 2.9 only: False error (missing "]" character) when a reject_{rhs,dns}bl_* or permit_{rhs,dns}wl_* reply pattern started with "[". Reported by Martijn Brinkers. Postfix 2.8 and later: The postscreen_access_list feature failed to ignore case in the first character of a command (e.g., permit, reject, etc.). Reported by Francis Picabia. (This fix is incorrectly listed in the HISTORY files of earlier releases, and will be removed with a future patch.) All supported releases: Strip the datalink suffix (e.g., %eth0) from IPv6 addresses returned by the system getaddrinfo() routine. Such suffixes break the default mynetworks value, the Postfix SMTP server's reverse/forward DNS name/address mapping check, and possibly more. To eliminate the possibility of collisions with connection cache lookup keys, the Postfix LDAP client now computes those lookup keys by joining the number-valued connection properties with ASCII null, just like it already did with the string-valued connection properties. There was a memory leak during one-time TLS library initialization (introduced with Postfix 2.5). Reported by Coverity. There was a memory leak in the unused oqmgr(8) program (introduced with Postfix 2.3). Reported by Coverity.
投票数:52 平均点:4.23
2012-12-11 sambaのupdate
2012-12-17 ImageMagickのupdate


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SeasonedWords, LLC
We offer a 15% discount to members of the Rabbit Room and to members of HSLDA. If you have been involved in a homeschool (teacher, student, teacher's helper, etc.) for two years or more, but are not currently a member of HSLDA you are still eligible to receive our discount.
proofreading checks:
We charge by the hour. Each book is an entity in itself, and it is difficult to know how much time it will take us to edit your book. Depending on how much or how little work your project needs, the cost is likely to be somewhere between one to three cents a word.
If you are interested in utilizing our firm but need a clearer price quote, send us three sample pages of your work. We will go over them for free, letting you see what we do, and allowing us to give you a better estimate of our charge for your particular book. We are open to splitting fees, allowing you to pay half earlier in the process, and the rest when we send your book back to you.
We perform a comprehensive edit if you contract to send us your book. This includes proofreading for spelling and grammatical errors, stylistic issues, character consistency, readability, plot believability, focus, clichés, a certain amount of fact checking, and more. Basically, if Seasoned Words, LLC, agrees to take on your book, we are agreeing to help you improve it as much as we can. Colossians 3:23 is our philosophy in our work: "And whatsoever you do, do it heartily, as unto the Lord, and not unto men." Besides, we are book-lovers, and get excited over the idea of a good, new book. We want to see yours become as good as it can.
All of our edits are tracked unless requested otherwise - we make suggestions and send the document back. You, the author, choose what to implement, and input it into your work. If you wish us to actually do the leg-work of making the changes in your book, you will have to specifically request it.
A Comprehensive edit includes:


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Statement from Governor Andrew M. Cuomo on Agreement Reached by REBNY and the Building Trades
Governor Andrew M. Cuomo today released the following statement on the deal reached by the Real Estate Board of New York and the Building and Construction Trades Council of Greater New York on the affordable housing program known as 421-a.
"The deal reached today between these parties provides more affordability for tenants and fairer wages for workers than under the original proposal. While I would prefer even more affordability in the 421-a program, this agreement marks a major step forward for New Yorkers. The agreement extends affordability for projects created with 421-a for an additional five years – bringing affordability for these units to 40 years. It also allows lower-income individuals to qualify as it lowers the percentage of area median income needed to apply.
"Additionally, this agreement rightly delivers fair wages for working men and women – providing a rate of $60 per hour in Manhattan and $45 for certain projects in Brooklyn and Queens. Most importantly until this agreement is finalized, the State Legislature has refused to release $2 billion in state affordable housing funds. I urge the Legislature to come back to Albany to pass desperately needed affordable housing and to sign the MOU to release these funds. We simply cannot allow the lack of resolution to stall affordable housing production for years to come. There is no excuse not to act."
Next Section
Spanish Translation Traducción al español
Russian Translation Перевод на русский язык
Korean Translation 한국어 번역
Italian Translation Traduzione italiana
Haitian Creole Translation Tradiksyon kreyòl ayisyen
French Translation Traduction française
Chinese Translation 中文翻譯
Next Section


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To make a long-term booking on certain days of the week only:
1. Search using the latest possible end date you think you may be parking. (You can always change this later!)
2. On the booking screen, select the option 'I would like a recurring weekly or monthly booking lasting longer than 6 weeks'.
3. Select the days of the week you want to park.
4. Pay now for the first month. Subsequent payments will be taken on a monthly basis for the duration of your booking.
Rather watch a video?


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Engagement photos
I recently used Sierra for an engagement on the beach. From the start Sierra was great with constant communication and timely response. She helped me plan a staged area on the beach and arrived early to set everything and make sure no one would ruin any photos. When we arrived to spot it was perfect and Sierra did an amazing job capturing the moment. We received the photos much quicker then we expected and everyone who has seen them has raved about amazing they look. I would without hesitation recommended Sierra for any photography you need done.
Sierra is amazing! We had such a wonderful experience at our engagement shoot and on our wedding day! We also received the pictures via an email link within 24 hrs of each event. We will be using her again for additional photo shoots!