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Entropic cohering power in quantum operations

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Abstract

Coherence is a basic feature of quantum systems and a common necessary condition for quantum correlations. It is also an important physical resource in quantum information processing. In this paper, using relative entropy, we consider a more general definition of the cohering power of quantum operations. First, we calculate the cohering power of unitary quantum operations and show that the amount of distributed coherence caused by non-unitary quantum operations cannot exceed the quantum-incoherent relative entropy between system of interest and its environment. We then find that the difference between the distributed coherence and the cohering power is larger than the quantum-incoherent relative entropy. As an application, we consider the distributed coherence caused by purification.

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Acknowledgements

Z. Xi is supported by the NSFC (Grant Nos. 61671280 and 11531009), the Natural Science Basic Research Plan in Shaanxi Province of China (No. 2017KJXX-92), the Funded Projects for the Academic Leaders and Academic Backbones, Shaanxi Normal University (16QNGG013) and the Fundamental Research Funds for the Central Universities (GK201502004). M. Hu is supported by the NSFC (Grant No. 11675129). Y. Li is supported by the NSFC (Grant No. 11671244). H. Fan is supported by MOST of China (2016YFA0302104), NSFC (Grant No. 91536108), and CAS (XDB01010000, XDB21030300).

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Authors and Affiliations

  1. College of Computer Science, Shaanxi Normal University, Xi’an, 710062, China

    Zhengjun Xi & Yongming Li

  2. School of Science, Xi’an University of Posts and Telecommunications, Xi’an, 710061, China

    Ming-Liang Hu

  3. Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China

    Heng Fan

  4. School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 100190, China

    Heng Fan

  5. Collaborative Innovation Center of Quantum Matter, Beijing, 100190, China

    Heng Fan

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  1. Zhengjun Xi
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  2. Ming-Liang Hu
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Correspondence to Zhengjun Xi.

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Xi, Z., Hu, ML., Li, Y. et al. Entropic cohering power in quantum operations. Quantum Inf Process 17, 34 (2018). https://doi.org/10.1007/s11128-017-1803-8

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  • DOI: https://doi.org/10.1007/s11128-017-1803-8

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