论复合量子系统特性的局部连续性

Pub Date : 2024-07-11 DOI:10.1134/s0081543824010206

M. E. Shirokov

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引用次数: 0

摘要

摘要考虑了对无穷维复合量子系统特性进行局部连续性分析的一般方法。提出并详细描述了一种新的近似技术，用于获得量子系统各种特性的局部连续性条件。利用这种技术证明了几个一般结果（西蒙式主导收敛定理、凸混合物下连续性保持定理等）。针对复合量子系统的以下特征推导出了局部连续性条件：量子条件熵、量子（条件）互信息、单向经典相关性及其正则化、量子不和及其正则化、形成的纠缠及其正则化，以及部分踪迹的受约束 Holevo 容量及其正则化。

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On Local Continuity of Characteristics of Composite Quantum Systems

Abstract

General methods of local continuity analysis of characteristics of infinite-dimensional composite quantum systems are considered. A new approximation technique for obtaining local continuity conditions for various characteristics of quantum systems is proposed and described in detail. This technique is used to prove several general results (a Simon-type dominated convergence theorem, a theorem on the preservation of continuity under convex mixtures, etc.). Local continuity conditions are derived for the following characteristics of composite quantum systems: the quantum conditional entropy, the quantum (conditional) mutual information, the one-way classical correlation and its regularization, the quantum discord and its regularization, the entanglement of formation and its regularization, and the constrained Holevo capacity of a partial trace and its regularization.

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