Quantum conditional entropy for infinite-dimensional systems

Abstract

In this paper a general definition of quantum conditional entropy for infinite-dimensional systems is given based on recent work of Holevo and Shirokov arXiv:1004.2495 devoted to quantum mutual and coherent informations in the infinite-dimensional case. The properties of the conditional entropy such as monotonicity, concavity and subadditivity are also generalized to the infinite-dimensional case.

8 pages

References in corpus (2)

• Information transmission through a noisy quantum channel
• Mutual and coherent informations for infinite-dimensional quantum channels

Cited by in corpus (20)

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• Position-Momentum Uncertainty Relations in the Presence of Quantum Memory
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• Tight continuity bounds for the quantum conditional mutual information, for the Holevo quantity and for capacities of quantum channels
• Entropy of a quantum channel
• Wehrl entropy, entropic uncertainty relations and entanglement
• Measures of quantum correlations in infinite-dimensional systems
• Energy-constrained two-way assisted private and quantum capacities of quantum channels
• Squashed entanglement in infinite dimensions
• Adaptation of the Alicki-Fannes-Winter method for the set of states with bounded energy and its use
• Optimal uniform continuity bound for conditional entropy of classical--quantum states
• Advanced Alicki-Fannes-Winter method for energy-constrained quantum systems and its use
• Quantum Brascamp-Lieb Dualities
• Continuity of characteristics of composite quantum systems
• Uniform continuity bounds for characteristics of multipartite quantum systems
• Close-to-optimal continuity bound for the von Neumann entropy and other quasi-classical applications of the Alicki-Fannes-Winter technique
• Uniform finite-dimensional approximation of basic capacities of energy-constrained channels
• On lower semicontinuity of the quantum conditional mutual information and its corollaries
• On discontinuity of information characteristics of quantum systems and channels