期刊
IEEE TRANSACTIONS ON INFORMATION THEORY
卷 69, 期 9, 页码 5857-5868出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2023.3277808
关键词
Quantum error correcting code; Singleton bound; entanglement-assisted code; hybrid code
This article discusses the derivation of Singleton bounds on the performance of entanglement-assisted hybrid classical-quantum error correcting codes using quantum Shannon theoretic methods. It shows that the triple-rate region of possible EACQ codes is contained within the quantum Shannon theoretic rate region of a memoryless erasure channel, which is a polytope. The study demonstrates that a large part of this region can be achieved by certain EACQ codes under certain conditions.
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 maximum 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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