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Optimal probabilistic cloning of two linearly independent states with arbitrary probability distribution

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Abstract

We investigate the probabilistic quantum cloning (PQC) of two states with arbitrary probability distribution. The optimal success probabilities are worked out for \(1\rightarrow 2\) PQC of the two states. The results show that the upper bound on the success probabilities of PQC in Qiu (J Phys A 35:6931–6937, 2002) cannot be reached in general. With the optimal success probabilities, we design simple forms of \(1\rightarrow 2\) PQC and work out the unitary transformation needed in the PQC processes. The optimal success probabilities for \(1\rightarrow 2\) PQC are also generalized to the \(M\rightarrow N\) PQC case.

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Acknowledgments

This work is supported by the 211 Project of Anhui University, the National Science Foundation of Anhui province (1508085MKL03, 1508085MF136) and the National Science Foundation of China (11374013).

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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, Ziyun Zhang & Yanlin Liao

  2. Anhui Xinhua University, Hefei, 230088, China

    Pinshu Rui

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  1. Wen Zhang
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  2. Pinshu Rui
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  3. Ziyun Zhang
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  4. Yanlin Liao
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Correspondence to Wen Zhang.

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Zhang, W., Rui, P., Zhang, Z. et al. Optimal probabilistic cloning of two linearly independent states with arbitrary probability distribution. Quantum Inf Process 15, 969–979 (2016). https://doi.org/10.1007/s11128-015-1170-2

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  • DOI: https://doi.org/10.1007/s11128-015-1170-2

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