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Maximum relative entropy of coherence for quantum channels

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Abstract

Based on the resource theory for quantifying the coherence of quantum channels, we introduce a new coherence quantifier for quantum channels via maximum relative entropy. We prove that the maximum relative entropy for coherence of quantum channels is directly related to the maximally coherent channels under a particular class of superoperations, which results in an operational interpretation of the maximum relative entropy for coherence of quantum channels. We also introduce the conception of sub-superchannels and sub-superchannel discrimination. For any quantum channels, we show that the advantage of quantum channels in sub-superchannel discrimination can be exactly characterized by the maximum relative entropy of coherence for quantum channels. Similar to the maximum relative entropy of coherence for channels, the robustness of coherence for quantum channels has also been investigated. We show that the maximum relative entropy of coherence for channels provides new operational interpretations of robustness of coherence for quantum channels and illustrates the equivalence of the dephasing-covariant superchannels, incoherent superchannels, and strictly incoherent superchannels in these two operational tasks.

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Author notes

  1. These authors contributed equally to this work.

Authors and Affiliations

  1. School of Physics, University of Chinese Academy of Sciences, Beijing, 100049, China

    Zhi-Xiang Jin & Cong-Feng Qiao

  2. State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing, 100084, China

    Long-Mei Yang & Gui-Lu Long

  3. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China

    Shao-Ming Fei & Zhi-Xi Wang

  4. Max-Planck-Institute for Mathematics in the Sciences, Leipzig, 04103, Germany

    Zhi-Xiang Jin, Shao-Ming Fei & Xianqing Li-Jost

  5. Frontier Science Center for Quantum Information, Beijing, 100084, China

    Gui-Lu Long

  6. Beijing National Research Center for Information Science and Technology, Beijing, 100084, China

    Gui-Lu Long

  7. Beijing Academy of Quantum Information Sciences, Beijing, 100193, China

    Gui-Lu Long

  8. CAS Center for Excellence in Particle Physics, Beijing, 100049, China

    Cong-Feng Qiao

Authors
  1. Zhi-Xiang Jin
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  2. Long-Mei Yang
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  3. Shao-Ming Fei
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  4. Xianqing Li-Jost
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  5. Zhi-Xi Wang
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  6. Gui-Lu Long
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Corresponding authors

Correspondence to Shao-Ming Fei or Cong-Feng Qiao.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11847209, 61727801, and 12075159), the China Postdoctoral Science Foundation (Grant No. 2019M650811), the China Scholarship Council (Grant No. 201904910005), Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology (Grant No. SIQSE202001), Beijing Natural Science Foundation (Grant No. Z190005), the Academician Innovation Platform of Hainan Province, and Academy for Multidisciplinary Studies, Capital Normal University.

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The supporting information is available online at phys.scichina.com and link.springer.com. The supporting materials are published as submitted, without typesetting or editing. The responsibility for scientific accuracy and content remains entirely with the authors.

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Jin, ZX., Yang, LM., Fei, SM. et al. Maximum relative entropy of coherence for quantum channels. Sci. China Phys. Mech. Astron. 64, 280311 (2021). https://doi.org/10.1007/s11433-021-1709-9

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  • DOI: https://doi.org/10.1007/s11433-021-1709-9

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