Singleton Bounds for Entanglement-Assisted Classical and Quantum Error Correcting Codes

• URL: http://arxiv.org/abs/2202.02184v4
• Date: Sun, 19 Mar 2023 16:15:49 GMT
• Title: Singleton Bounds for Entanglement-Assisted Classical and Quantum Error Correcting Codes
• Authors: Manideep Mamindlapally, Andreas Winter
• Abstract summary: We show that entirely quantum Shannon theoretic methods can be used to derive Singleton bounds on the performance of EACQ error correcting codes. We show that a large part of this region is attainable by certain EACQ codes, whenever the local alphabet size is large enough.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We show that entirely quantum Shannon theoretic methods, based on von Neumann entropies and their properties, can be used to derive Singleton bounds on the performance of entanglement-assisted hybrid classical-quantum (EACQ) error correcting codes. Concretely, we show that the triple-rate region of qubits, cbits and ebits of possible EACQ codes over arbitrary alphabet sizes is contained in the quantum Shannon theoretic rate region of an associated memoryless erasure channel, which turns out to be a polytope. We show that a large part of this region is attainable by certain EACQ codes, whenever the local alphabet size (i.e. Hilbert space dimension) is large enough, in keeping with known facts about classical and quantum minimum distance separable (MDS) codes: in particular, all of its extreme points and all but one of its extremal lines. The attainability of the remaining one extremal line segment is left as an open question.

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