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Quantification of resource theory of imaginarity

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Abstract

Complex numbers are indispensable parts of describing states of quantum systems and their dynamic behavior, and they are widely used in classical and quantum physics. In recent years, some studies and experiments have shown the necessity of complex numbers in quantum physics. In this work, we investigate the quantification of imaginarity and explore connections of several properties of imaginary measures. In addition, we focus on two specific imaginarity measures: the weight of imaginarity and the relative entropy of imaginarity, proving that they have some nice properties. We also study the corresponding semidefinite programming form of the weight of imaginarity and obtain a closed expression of the relative entropy of imaginarity. Moreover, we analyze the quantitative relationships of several imaginarity measures. Our work further studies the quantification of imaginarity, and provides two concrete measures with interesting properties for imaginarity, which will contribute to the development of quantum mechanics and quantum technology.

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Acknowledgements

This paper was supported by Fundamental Research Funds for the Central Universities (Grant No.: GK201703002) and National Science Foundation of China (Grant Nos.: 12071271, 11671244).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Shaanxi Normal University, Xi’an, 710062, China

    Shengnan Xue, Jiansheng Guo, Mingfei Ye & Yongming Li

  2. School of Computer Science, Shaanxi Normal University, Xi’an, 710062, China

    Ping Li

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  1. Shengnan Xue
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  2. Jiansheng Guo
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Correspondence to Jiansheng Guo.

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Xue, S., Guo, J., Li, P. et al. Quantification of resource theory of imaginarity. Quantum Inf Process 20, 383 (2021). https://doi.org/10.1007/s11128-021-03324-5

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