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Average distillated coherence without complete waste of resources

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Abstract

To distill quantum coherence, in [Phys. Rev. A 99, 012321 (2019)], authors proposed a strictly incoherent operation that produces one of a family of maximally coherent states of variable dimension from any pure quantum state. For a d-dimensional pure state, an incoherent state may be obtained with a nonzero probability, which results in a complete waste of resource, namely the probability of transforming a given pure state to the incoherent state is not zero. Here, we give a specific method to avoid a complete waste of resource with the maximal probability to transform the pure state to a d-dimensional maximally coherent state and study the range of average coherence of the corresponding output state in this case. We also give a method to transform a mixed state to a maximally coherent state with probability.

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Acknowledgements

This work is supported by the NSF of China under Grant Nos. 12075159, 11847209, and 61727801; Academy for Multidisciplinary Studies, Capital Normal University; Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology (No. SIQSE202001); the Academician Innovation Platform of Hainan Province; Beijing Natural Science Foundation (Z190005); Beijing Advanced Innovation Center for Future Chip (ICFC); the Key R & D Program of Guangdong Province (2018B030325002); the China Postdoctoral Science Foundation funded Project No. 2019M650811 and the China Scholarship Council No. 201904910005.

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Authors and Affiliations

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

    Long-Mei Yang & Gui-Lu Long

  2. School of Physics, University of Chinese Academy of Science, Beijing, 100049, China

    Zhi-Xiang Jin

  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, 04103, Leipzig, Germany

    Zhi-Xiang Jin & Shao-Ming Fei

  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

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  1. Long-Mei Yang
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Correspondence to Zhi-Xiang Jin.

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Yang, LM., Jin, ZX., Fei, SM. et al. Average distillated coherence without complete waste of resources. Quantum Inf Process 20, 198 (2021). https://doi.org/10.1007/s11128-021-03137-6

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