Explicit convergence rates for noncommutative SOS hierarchies on the Pauli algebra are bounded using smallest roots of Krawtchouk polynomials.
Quantum MacWilliams Identities
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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, 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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quant-ph 1years
2026 1verdicts
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Convergence rates of Sum-of-Hermitian-Squares Hierarchies for the Pauli algebra
Explicit convergence rates for noncommutative SOS hierarchies on the Pauli algebra are bounded using smallest roots of Krawtchouk polynomials.