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The Transformation From Pure States to X States Under Incoherent Operations

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Abstract

We study the conversion between pure states and X states under incoherent operations. We derive an optimal pure state decomposition of X state such that all pure state decompositions of X state are majorized by it. Then we show a necessary and sufficient condition for pure states which can be converted into X state under incoherent operations. We also obtain an optimal pure state related to X state such that all pure states that can be converted to X state by incoherent operations are majorized by it. The incoherent operations converting the pure state into X state are analyzed. The coherence measure is also calculated for X states.

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Acknowledgements

Ming-Jing Zhao is supported by Qin Xin Talents Cultivation Program, Beijing Information Science and Technology University. Ting-Gui Zhang is supported by the National Natural Science Foundation of China under Grant No. 11861031, the “Academician Innovation Platform” of Hainan Province and Key Laboratory Of Data Science And Smart Education (Hainan Normal University), Ministry of Education.

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Authors and Affiliations

  1. School of Science, Beijing Information Science and Technology University, Beijing, 100192, China

    Ying Wang & Ming-Jing Zhao

  2. School of Mathematics and Statistics, Hainan Normal University, Haikou, 571158, People’s Republic of China

    Ting-Gui Zhang

  3. Hainan Center for Mathematical Research, Hainan Normal University, Haikou, 571158, People’s Republic of China

    Ting-Gui Zhang

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  1. Ying Wang
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  2. Ming-Jing Zhao
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Correspondence to Ming-Jing Zhao.

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Wang, Y., Zhao, MJ. & Zhang, TG. The Transformation From Pure States to X States Under Incoherent Operations. Int J Theor Phys 60, 2976–2985 (2021). https://doi.org/10.1007/s10773-021-04884-z

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  • DOI: https://doi.org/10.1007/s10773-021-04884-z

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