Entropic cohering power in quantum operations

  • Zhengjun Xi
  • Ming-Liang Hu
  • Yongming Li
  • Heng Fan


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.


Coherence Quantum correlations Distributed coherence Quantum operation 



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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Zhengjun Xi
    • 1
  • Ming-Liang Hu
    • 2
  • Yongming Li
    • 1
  • Heng Fan
    • 3
    • 4
    • 5
  1. 1.College of Computer ScienceShaanxi Normal UniversityXi’anChina
  2. 2.School of ScienceXi’an University of Posts and TelecommunicationsXi’anChina
  3. 3.Beijing National Laboratory for Condensed Matter Physics, Institute of PhysicsChinese Academy of SciencesBeijingChina
  4. 4.School of Physical SciencesUniversity of Chinese Academy of SciencesBeijingChina
  5. 5.Collaborative Innovation Center of Quantum MatterBeijingChina

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