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Assisted Coherence Distillation of Certain Mixed States

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Abstract

We study the assisted coherence distillation of two special classes of mixed states including the states with vanished basis-dependent discord in the incoherent basis of the second party and Werner two-qubit states via the sets of operations such as local incoherent operations and classical communication (LICC), local quantum-incoherent operations and classical communication (LQICC), separable incoherent operations (SI), and separable quantum-incoherent operations (SQI). We show that the assisted distillable coherence of the former can reach the upper bound, namely quantum-incoherent (QI) relative entropy via all the sets of operations considered above. In contrast, for the Werner two-qubit states the assisted distillable coherence is strictly smaller than the quantum-incoherent (QI) relative entropy. Our results also mean that the optimal rate of assisted coherence distillation of Werner two-qubit states can be achieved even in one-copy scenarios without the complex joint quantum operations on many copies. Finally, we discuss the coherence location in the multipartite system.

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Acknowledgements

We thank Zheng-Jun Xi for useful discussion. This work is supported by the National Natural Science Foundation of China (Grants Nos. 61972048, 61976024, 61601171, and 11971151).

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Authors and Affiliations

  1. State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Xiao-Li Wang & Su-Juan Qin

  2. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, 454000, China

    Xiao-Li Wang & Ying-Hui Yang

  3. School of Computer Science and Cyberspace Security (School of Cryptogram), Hainan University, Haikou, 570228, China

    Qiu-Ling Yue

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  1. Xiao-Li Wang
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Correspondence to Su-Juan Qin.

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Wang, XL., Yue, QL., Yang, YH. et al. Assisted Coherence Distillation of Certain Mixed States. Int J Theor Phys 61, 34 (2022). https://doi.org/10.1007/s10773-022-05010-3

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