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.
Keywords:
quantum state, von Neumann entropy, correlation measure, entanglement measure, locally almost affine function, quantum channel, quantum measurement.
Citation:
M. E. Shirokov, “On Local Continuity of Characteristics of Composite Quantum Systems”, Noncommutative Analysis and Quantum Information Theory, Collected papers. Dedicated to Academician Alexander Semenovich Holevo on the occasion of his 80th birthday, Trudy Mat. Inst. Steklova, 324, Steklov Math. Inst., Moscow, 2024, 238–276; Proc. Steklov Inst. Math., 324 (2024), 225–260
\Bibitem{Shi24}
\by M.~E.~Shirokov
\paper On Local Continuity of Characteristics of Composite Quantum Systems
\inbook Noncommutative Analysis and Quantum Information Theory
\bookinfo Collected papers. Dedicated to Academician Alexander Semenovich Holevo on the occasion of his 80th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2024
\vol 324
\pages 238--276
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4383}
\crossref{https://doi.org/10.4213/tm4383}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=4767961}
\zmath{https://zbmath.org/?q=an:1543.81028}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2024
\vol 324
\pages 225--260
\crossref{https://doi.org/10.1134/S0081543824010206}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85198125848}
Citation in format AMSBIB
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