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The Tsallis Relative 2-Entropy of Coherence under Mutually Unbiased Bases

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Abstract

The performance of quantum coherence under different bases is an important subject in quantum theory and quantum information science. This paper mainly focuses on the Tsallis relative 2-entropy of coherence of quantum states under mutually unbiased bases(MUBs) in two, three and four dimensional systems. For single-qubit mixed states, the sum under complete MUBs is less than \(\sqrt{6}\); for Gisin states and Bell-diagonal states in four dimensional system, the sum under a new set of “autotensor of mutually unbiased basis” (AMUBs) is less than nine. For three classes of X states in three-dimensional system, each Tsallis relative 2-entropy of coherence under nontrivial unbiased bases is found equal. Also the surfaces of the sum of the Tsallis relative 2-entropy of coherence under MUBs and AMUBs are described, respectively. Among them, a surface of a special class of X states in AMUBs is an ellipsoid.

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Authors and Affiliations

  1. Department of Mathematics, College of Sciences, Yanbian University, Yanji, 133002, China

    Liu Sun & Lin Song Li

  2. Department of Big Data, College of Science, Zhejiang University of Science and Technology, Hangzhou, Zhengjiang, 310023, China

    Yuan-Hong Tao

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  1. Liu Sun
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Liu Sun and Yuanhong Tao wrote the main manuscript text. All of the authors reviewed the manuscript

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Correspondence to Yuan-Hong Tao.

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Sun, L., Tao, YH. & Li, L.S. The Tsallis Relative 2-Entropy of Coherence under Mutually Unbiased Bases. Int J Theor Phys 62, 167 (2023). https://doi.org/10.1007/s10773-023-05408-7

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