In chapter 1 of Quantum Computation and Quantum Information by Michael A. Nielsen &amp; Isaac L. Chuang, I came across this paragraph on quantum teleportation,  Intuitively, things look pretty bad for Alice. She doesn’t know the state $\lvert\psi\rangle$ of the qubit she has to send to Bob, and the laws of quantum mechanics prevent her from determining the state when she only has a single copy of $\lvert\psi\rangle$ in her possession. What’s worse, even if she did know the state $\lvert\psi\rangle$, describing it precisely takes an infinite amount of classical information since $\lvert\psi\rangle$ takes values in a continuous space. So even if she did know $\lvert\psi\rangle$, it would take forever for Alice to describe the state to Bob.  So Alice and Bob share a qubit each from an EPR pair created long ago and now Alice wishes to teleport the state $\lvert\psi\rangle$ to Bob by only sending classical information. I do not understand why describing $\lvert\psi\rangle$ takes an infinite amount of classical information, since to my knowledge, only the amplitudes of the basis vectors need to be known($\lvert\psi\rangle=\alpha \lvert 0\rangle+\beta \lvert 1\rangle$). Maybe I did not understand properly what it means for Alice to know a state $\lvert\psi\rangle$. Any guidance would be helpful. Thank you. PS: I'm not from a Quantum mechanics background.
I have two question concerning information content of qubit.  Question 1: How many classical bits are needed to represent a qubit:  A qubit can be represented by a vector $q = \begin{pmatrix}\alpha \\\beta \end{pmatrix}, ~~ \alpha, \beta \in \mathbb{C}$. So, we need four real numbers to represent it. But when facts that (i) $|\alpha|^2+|\beta|^2 = 1$ and (ii) two qubits which differ in global phase only are indistinguishable, are taken into account, only two real numbers are necessary (angles on Bloch sphere). Moreover, we can choose a precission of the qubit representation (i.e. number of decimal places in $\alpha$ and $\beta$ or Bloch sphere angles) which influence number of classical bits needed to described the qubit.   So, it seems to me that the qubit representation cannot be used for measuring qubit information content but only memory consumption in simulation. Am I right?  Question 2: What is an (effective) information content of qubit:  A superdense coding enable us to send two classical bits via one qubit. But on the other hand you need two entangled qubits prepared in advance.  Given these facts, what is an information content of qubit? One or two classical bits? Or do I need to use another angle of view given the fact that qubits are "continuous" (i.e. described by complex numbers $\alpha$ and $\beta$)?
Trying to find a story about an unborn telepathic baby who can save a spaceship from doom There's a spaceship, nearing the end of its journey. Everybody on board is in cryosleep. For some reason the wake-up system malfunctions, and the ship will fly on indefinitely. The people at the space port realise this, and try to wake someone up. Their last resort is finding someone on board who is telepathic, and wake this person up. They find one, but it turns out to be an unborn baby. Difference between modelAttribute and commandName attributes in form tag in spring? Remove a child with a specific attribute, in SimpleXML for PHP I have several identical elements with different attributes that I'm accessing with SimpleXML:  &lt;data&gt;     &lt;seg id="A1"/&gt;     &lt;seg id="A5"/&gt;     &lt;seg id="A12"/&gt;     &lt;seg id="A29"/&gt;     &lt;seg id="A30"/&gt; &lt;/data&gt;   I need to remove a specific seg element, with an id of "A12", how can I do this?  I've tried looping through the seg elements and unsetting the specific one, but this doesn't work, the elements remain.  foreach($doc-&gt;seg as $seg) {     if($seg['id'] == 'A12')     {         unset($seg);     } } I have been following  tutorial until I started adding nodes. The problem is that he has completely different nodes than I have. Even nodes that are created at start are different (I have Material and Output and he has Render Layers and Composite). Have I missed something or should I use different nodes than he? How to add CC to a webform email? I'm using Drupal 7.  Is it possible to add a CC to a webform email?  I was using   function theme_webform_mail_headers($variables) {   $headers = array(     'X-Mailer' =&gt; 'Drupal Webform (PHP/' . phpversion() . ')',   );   return $headers; }   changing it with      function MYTHEME_webform_mail_headers($variables) {       $headers = array( 'CC' =&gt; 'ccmeail@domain.com', 'X-Mailer' =&gt; 'Drupal Webform (PHP/'. phpversion() .')',  );       return $headers;     }   It does not work, I've cleared all the chaches and it does not add the CC. How could I add the CC?  Thanks in advance. Sometimes you just want to let out some steam, and troll about some technology or software. You are not looking for any answers, but for users with similar experiences and interesting stories. So why not create a separate discussion site (trolling.stackoverflow.com?), where you could ask questions like "why do you hate technology X" or "What are the stupidest bugs you encountered in X"? Why a tesselation of the plane by a convex polygon of 7 or more sides is not possible? I read in several places, including Wikipedia, that a tessellation of the plane by a single, convex, $n-$sided polygon is not possible for $n\geq7$. I was not able to locate a proof, or a paper that discusses this. Maybe it is too trivial, but I am not able to figure it out myself.   So I would like to ask you for help. Where can I find a proof for this?  Also, I am interested in the mathematical background behind plane tiling (especially periodic), If you can suggest papers on the topic it would really help. Making an invisible pressure plate I'm trying to build a teleporter. I want the player to be teleported from the first sign(left) to the right sign(right). So, when the player steps on the red wool on the left, he will automatically be teleported to the red wool on the right. I do not want to use any pressure plats.It might work with the testfor comment, but I didn't figure out, put that only works with a radius. BTW I'm in 1.10.2 bou I could probably change the version if necessary.     The testfor command block should activate the teleport command block,when the player is detected. Now, I'm not really the expert, so I know non of the commands that you would need to build this construction. Please help, I would highly appreciate it! If you need any more details, ask me! BufferedWriter not writing everything to its output file Black screen after suspend-after moving to the nvidia official drivers (not priority) So, when I used the priority drivers, the suspend worked normal. But the official drivers works better, so I installed the official driver. Then suspend won't work.  Should I change any text/documants to make it work? Any solution will be aprreciated, thanks you all! WP_query 'orderby=none' Problem I have another database which stores post's IDs and I want do display them using WP_query to use the WP default pagination. I'm using orderby => none to preserve the original order, but the result reorders them by IDs.  $ids = array (60, 23, 78, 46, 105, 130)  $args = array (     'posts_per_page' =&gt; -1,     'post__in' =&gt; $ids,     'orderby' =&gt; 'none' );  $query = new WP_Query ( $args );  while ( have_posts() ) : the_post();     echo '&lt;li&gt;';     the_title();     echo '&lt;/li&gt;'; endwhile;   Could anyone help me?  Thanks, Romulo De Lazzari What mechanism is responsible for the creation of these dunes on Comet 67P/Churyumov-Gerasimenko?  The following high resolution picture from ESA's Rosetta mission shows the dunes:       At a distance of 7.8 km from the surface, the image scale is about   66.5 cm/pixel, so each 1024 x 1024 pixel frame is about 680 m across (although if we assume the furthest point away is an additional ~1 km   further from the centre, the image scale is about 92 cm/pixel).   So the scale of the dunes is on the order of tens of meters along the crest. And each crest are probably just a few meters apart. How can phone companies detect tethering (incl. Wifi hotspot) How to switch between low latency and generic kernels? Is adjusting p-values in a multiple regression for multiple comparisons a good idea? Lets assume you are a social science researcher/econometrician trying to find relevant predictors of demand for a service. You have 2 outcome/dependent variables describing the demand (using the service yes/no, and the number of occasions). You have 10 predictor/independent variables that could theoretically explain the demand (e.g., age, sex, income, price, race, etc). Running two separate  multiple regressions will yield 20 coefficients estimations and their p-values. With enough independent variables in your regressions you would sooner or later find at least one variable with a statistically significant correlation between the dependent and independent variables.   My question: is it a good idea to correct the p-values for multiple tests if I want to include all independent variables in the regression? Any references to prior work are much appreciated. Undo git pull, how to bring repos to old state MySQL get missing IDs from table Can I add extension methods to an existing static class? I'm a fan of extension methods in C#, but haven't had any success adding an extension method to a static class, such as Console.  For example, if I want to add an extension to Console, called 'WriteBlueLine', so that I can go:  Console.WriteBlueLine("This text is blue");   I tried this by adding a local, public static method, with Console as a 'this' parameter... but no dice!      public static class Helpers {     public static void WriteBlueLine(this Console c, string text)     {         Console.ForegroundColor = ConsoleColor.Blue;         Console.WriteLine(text);         Console.ResetColor();     } }   This didn't add a 'WriteBlueLine' method to Console... am I doing it wrong? Or asking for the impossible? Is it possible to interrupt spellcasting? Why are polymorphic values not inferred in Haskell?