论文标题
纠缠辅助经典和量子错误纠正代码的单例界限
Singleton Bounds for Entanglement-Assisted Classical and Quantum Error Correcting Codes
论文作者
论文摘要
我们表明，基于von Neumann熵及其特性，完全量子香农理论方法可用于在纠缠辅助混合经典Quantum（EACQ）错误校正代码的性能上得出单身界的界限。具体而言，我们表明，在任意字母大小上可能的EACQ代码的Qubit，CBIT和EBITS的三率区域包含在相关无内存擦除通道的量子香农理论率区域中，事实证明，这是多层。我们表明，每当局部字母大小（即希尔伯特空间维度）足够大时，可以通过某些EACQ代码来实现该区域的很大一部分，这与有关经典和量子最小距离（MDS）代码的已知事实保持一致：尤其是其极端点，除了其极端线之外。其余一条极端线段的可达到性是一个悬而未决的问题。
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.
