For example, the simplified logical matrix corresponding to the initial state | ψ 〉 EA is    O$_{k}$ × n O$_{k}$ × r I$_{k}$ × k O$_{k}$ × r I$_{k}$ × k O$_{k}$ × n    . (16) 3 The Encoding Optimization Procedure for EAQECCs A standard [[ n, 2 k − n, d ]] quantum stabilizer code, obtained by the CSS construction [7, 8] from an [ n, k, d ] classical linear self-orthogonal code, has the same minimum distance as the classical code used. On the other hand, an [[ n, 2 k + c − n, d ; c ]] EAQEC code can be constructed from an [ n, k, d ] classical linear quaternary code by the construction of [10], and c is determined by (14). It seems that only the number of information qubits is increased by introducing ebits. However, with the help of entanglement it is possible to define more distinct error syndromes for a given codeword size, and hence the set of correctable error operators might be larger. We would like to construct EAQEC codes with a higher minimum distance instead of higher rate. One way to construct an EAQEC code is to start with a standard QECC and move c of the qubits from Alice’s side to Bob’s side. So long as c ≤ d/ 2, the resulting code can be encoded by a unitary operator on Alice’s side, given c ebits of initial shared entanglement between Alice and Bob. While such codes can be interesting and useful, they are not the subject of interest for this paper; because such codes retain an ability to correct errors on Bob’s qubits, they are in a sense not making full use of the fact that Bob’s halves of the ebits are noise-free. They therefore may not have the maximum error correcting power on Alice’s qubits for the given parameters n , k and c . We are interested in EAQEC codes that can do better than any standard code in this sense. To make this idea precise, we say that an [[ n, k, d ; c ]] EAQEC code is not equivalent to any standard quantum stabilizer code if there is no standard [[ n + c, k, d ]] quantum code. 13