Derives closed-form MacWilliams matrix for permutation-invariant qudit codes as Racah polynomials with parameters set by block length and dimension.
Pauli exchange errors in quantum computation
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Intrinsic MacWilliams identities are introduced for quantum codes in group representations, yielding linear programming bounds on permutation-invariant qubit and qudit codes.
A quantum anonymous secret sharing scheme is constructed using permutation-invariant codes, with leakage in ramp schemes quantified by quantum conditional min-entropy related to Knill-Laflamme conditions.
citing papers explorer
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Orthogonal Polynomials and the MacWilliams Transform for Permutation-Invariant Qudit Codes
Derives closed-form MacWilliams matrix for permutation-invariant qudit codes as Racah polynomials with parameters set by block length and dimension.
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MacWilliams Identities for Intrinsic Quantum Codes
Intrinsic MacWilliams identities are introduced for quantum codes in group representations, yielding linear programming bounds on permutation-invariant qubit and qudit codes.
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Quantum Anonymous Secret Sharing with Permutation Invariant Codes
A quantum anonymous secret sharing scheme is constructed using permutation-invariant codes, with leakage in ramp schemes quantified by quantum conditional min-entropy related to Knill-Laflamme conditions.