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ENTROPY OF A QUANTUM ERROR CORRECTION CODE
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"... Abstract. We define and investigate a notion of entropy for quantum error correcting codes. The entropy of a code for a given quantum channel has a number of equivalent realisations, such as through the coefficients associated with the KnillLaflamme conditions and the entropy exchange computed with ..."
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Abstract. We define and investigate a notion of entropy for quantum error correcting codes. The entropy of a code for a given quantum channel has a number of equivalent realisations, such as through the coefficients associated with the KnillLaflamme conditions and the entropy exchange computed with respect to any initial state supported on the code. In general the entropy of a code can be viewed as a measure of how close it is to the minimal entropy case, which is given by unitarily correctable codes (including decoherencefree subspaces), or the maximal entropy case, which from dynamical Choi matrix considerations corresponds to nondegenerate codes. We consider several examples, including a detailed analysis in the case of binary unitary channels, and we discuss an extension of the entropy to operator quantum error correcting subsystem codes. 1.