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Probabilistic cloning of three nonorthogonal states

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Abstract

We study the probabilistic cloning of three nonorthogonal states with equal success probabilities. For simplicity, we assume that the three states belong to a special set. Analytical form of the maximal success probability for \(M\rightarrow N\) probabilistic cloning is calculated. With the maximal success probability, we deduce the explicit form of \(M\rightarrow N\) probabilistic quantum cloning machine. In the case of \(1\rightarrow 2\) cloning, we get the unambiguous form of the unitary operation. It is demonstrated that the upper bound for probabilistic quantum cloning machine in (Qiu in J Phys A 35:6931, 2002) can be reached only if the three states are equidistant.

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Acknowledgments

This work is supported by the 211 Project of Anhui University, the National Science Foundation of China (11374013), and the Anhui Provincial Natural Science Foundation (1408085QF127).

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Authors and Affiliations

  1. Key Laboratory of Optoelectronic Information Acquisition and Manipulation of Ministry of Education of China, School of Physics and Material Science, Anhui University, Hefei, 230601, China

    Wen Zhang, Qun Yang & Ziyun Zhang

  2. Anhui Xinhua University, Hefei, 230088, China

    Pinshu Rui

  3. Department of Physics, Anhui Medical University, Hefei, 230032, China

    Yan Zhao

Authors
  1. Wen Zhang
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  2. Pinshu Rui
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  3. Qun Yang
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  4. Yan Zhao
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  5. Ziyun Zhang
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Correspondence to Wen Zhang.

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Zhang, W., Rui, P., Yang, Q. et al. Probabilistic cloning of three nonorthogonal states. Quantum Inf Process 14, 1523–1534 (2015). https://doi.org/10.1007/s11128-015-0921-4

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  • DOI: https://doi.org/10.1007/s11128-015-0921-4

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