Progress on Problem about Quantum Hamming Bound for Impure Quantum Codes
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🪐 quant-ph
keywords
quantumcodesboundhammingproblemcodeimpurearbitrary
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A famous open problem in the theory of quantum error-correcting codes is whether or not the parameters of an impure quantum code can violate the quantum Hamming bound for pure quantum codes. We partially solve this problem. We demonstrate that there exists a threshold such that an arbitrary quantum code must obey the quantum Hamming bound whenever . We list some values of for small d and binary quantum codes.
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Cited by 1 Pith paper
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The Quantum Hamming Bound in Arbitrary Local Dimension
Proves the finite-length quantum Hamming bound for every nontrivial exact subspace code in local dimension q ≥ 3.
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