Quantum Analog of the MacWilliams Identities for Classical Coding Theory
- 24 February 1997
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 78 (8), 1600-1602
- https://doi.org/10.1103/physrevlett.78.1600
Abstract
We derive a relationship between two different notions of fidelity (entanglement fidelity and average fidelity) for a completely depolarizing quantum channel. This relationship gives rise to a quantum analog of the MacWilliams identities in classical coding theory. These identities relate the weight enumerator of a code to the one of its dual and, with linear programming techniques, provide a powerful tool to investigate the possible existence of codes. The same techniques can be adapted to the quantum case. We give examples of their power.Keywords
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