Geodesic
On Local Continuity of Characteristics of Composite Quantum Systems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Noncommutative Analysis and Quantum Information Theory, Tome 324 (2024), pp. 238-276

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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.
Keywords: quantum state, von Neumann entropy, correlation measure, entanglement measure, locally almost affine function, quantum channel, quantum measurement. 
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     author = {M. E. Shirokov},
     title = {On {Local} {Continuity} of {Characteristics} of {Composite} {Quantum} {Systems}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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     url = {http://geodesic.mathdoc.fr/item/TM_2024_324_a19/}
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M. E. Shirokov. On Local Continuity of Characteristics of Composite Quantum Systems. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Noncommutative Analysis and Quantum Information Theory, Tome 324 (2024), pp. 238-276. http://geodesic.mathdoc.fr/item/TM_2024_324_a19/