Quantifying quantum coherence based on the Tsallis relative operator entropy

Abstract

Coherence is a fundamental ingredient in quantum physics and a key resource in quantum information processing. The quantification of quantum coherence is of great importance. We present a family of coherence quantifiers based on the Tsallis relative operator entropy. Shannon inequality and its reverse one in Hilbert space operators derived by Furuta [Linear Algebra Appl. 381 (2004) 219] are extended in terms of the parameter of the Tsallis relative operator entropy. These quantifiers are shown to satisfy all the standard criteria for a well-defined measure of coherence and include some existing coherence measures as special cases. Detailed examples are given to show the relations among the measures of quantum coherence.

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Acknowledgements

This work is supported by NSFC under numbers 11765016, 11847209, 11675113, the GJJ170444, Key Project of Beijing Municipal Commission of Education (KZ201810028042), and Beijing Natural Science Foundation (Z190005), Academy for Multidisciplinary Studies, Capital Normal University, Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China (No. SIQSE202001), China Postdoctoral Science Foundation funded project No. 2019M650811 and the China Scholarship Council No. 201904910005.

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Correspondence to Meng-Li Guo.

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Guo, ML., Jin, ZX., Li, B. et al. Quantifying quantum coherence based on the Tsallis relative operator entropy. Quantum Inf Process 19, 382 (2020). https://doi.org/10.1007/s11128-020-02885-1

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Keywords

  • Quantum coherence
  • The Tsallis relative operator entropy