Abstract:
In quantum information theory, one needs to consider systems with incomplete information. To estimate a quantum system as an information resource, one uses various characteristics of non-classical correlations. Currently, much attention is paid to coherence quantifiers averaged over a set of specially selected states. In particular, mutually unbiased bases, symmetric informationally complete measurements, and some of their generalizations are of importance in this regard. The aim of the present study is to derive uncertainty relations for coherence quantifiers based on divergences of the Tsallis type. The obtained inequalities concern quantifiers averaged over a set of mutually unbiased bases and a set of states that form an equiangular tight frame.
Keywords:quantum coherence, index of coincidence, uncertainty principle, Tsallis entropy.
Citation:
A. E. Rastegin, “Uncertainty Relations for Coherence Quantifiers of the Tsallis Type”, 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, 188–197; Proc. Steklov Inst. Math., 324 (2024), 178–186
\Bibitem{Ras24}
\by A.~E.~Rastegin
\paper Uncertainty Relations for Coherence Quantifiers of the Tsallis Type
\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 188--197
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4379}
\crossref{https://doi.org/10.4213/tm4379}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4767958}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2024
\vol 324
\pages 178--186
\crossref{https://doi.org/10.1134/S0081543824010176}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85198115496}
Linking options:
https://www.mathnet.ru/eng/tm4379
https://doi.org/10.4213/tm4379
https://www.mathnet.ru/eng/tm/v324/p188
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