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Quantum MacWilliams Identities

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arxiv quant-ph/9610040 v1 pith:QW6LWVF2 submitted 1996-10-25 quant-ph

Peter Shor , Raymond Laflamme This is my paper · ORCID
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keywords quantumfidelityidentitiesmacwilliamsrelationshiptechniquesadaptedanalog
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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, provided 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.

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Cited by 1 Pith paper

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  1. Convergence rates of Sum-of-Hermitian-Squares Hierarchies for the Pauli algebra

    quant-ph 2026-06 unverdicted novelty 8.0 of 10

    Explicit convergence rates for noncommutative SOS hierarchies on the Pauli algebra are bounded using smallest roots of Krawtchouk polynomials.

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