Constructs minimal ((4,q,2))_q permutation-invariant qudit codes for every q >= 2 via edge-colorings of K_q and proves no such codes exist for n <= 3.
Pauli exchange errors in quantum computation
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Derives closed-form MacWilliams matrix for permutation-invariant qudit codes as Racah polynomials with parameters set by block length and dimension.
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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Minimal Permutation-Invariant Qudit Codes from Edge-Colorings of Complete Graphs
Constructs minimal ((4,q,2))_q permutation-invariant qudit codes for every q >= 2 via edge-colorings of K_q and proves no such codes exist for n <= 3.
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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.