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Random quantum evolution

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Abstract

The quantum no-cloning theorem and no-deleting theorem may be the most important quantum features for quantum communications or quantum computations. In this paper, we concentrate typical properties of random quantum evolution. We obtain that universal random evolutions change the generic unknown pure states into their orthogonal states approximately. Moreover, typical random evolutions distort the von Neumann entropy with constants. These results are extended to mixed states with a stronger orthogonal preparation ability. These typical characters are very important for quantum information retrieving or various quantum tasks.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China (Nos. 11226336, 61003287, 61170272, 61103198, 61272514, 61201253), the Fundamental Research Funds for the Central Universities (Nos. SWJTU11BR174, BUPT2012RC0221), the Fok Ying Tong Education Foundation No. 131067, the Specialized Research Fund for the Doctoral Program of Higher Education (20100005120002), the Natural Science Foundation of Henan Provincial Education Department (12A120003).

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Authors and Affiliations

  1. Information Security Center, Southwest Jiaotong University, Chengdu, 610031, China

    Ming-Xing Luo

  2. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, China

    Ming-Xing Luo & Xiu-Bo Chen

  3. Institute of Computer Science, Sichuan University of Science Engineering, Zigong, 64300, China

    Yun Deng

  4. School of Mathematics and Information Sciences, Henan University, Kaifeng, 475004, China

    Song-Ya Ma

  5. Information Security Center, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Xiu-Bo Chen

  6. Jiangsu Engineering Center of Network Monitoring, School of Computer and Software, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Zhi-Guo Qu

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  1. Ming-Xing Luo
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  2. Yun Deng
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Correspondence to Ming-Xing Luo.

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Luo, MX., Deng, Y., Ma, SY. et al. Random quantum evolution. Quantum Inf Process 12, 3353–3367 (2013). https://doi.org/10.1007/s11128-013-0603-z

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