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Unambiguous discrimination between linearly dependent equidistant states with multiple copies

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Abstract

Linearly independent quantum states can be unambiguously discriminated, but linearly dependent ones cannot. For linearly dependent quantum states, however, if C copies of the single states are available, then they may form linearly independent states, and can be unambiguously discriminated. We consider unambiguous discrimination among N = D + 1 linearly dependent states given that C copies are available and that the single copies span a D-dimensional space with equal inner products. The maximum unambiguous discrimination probability is derived for all C with equal a priori probabilities. For this classification of the linearly dependent equidistant states, our result shows that if C is even then adding a further copy fails to increase the maximum discrimination probability.

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Acknowledgements

This research was funded by the Natural Science Foundation of the Education Department of Anhui Province of China under Grants Nos. KJ2016A672 and KJ2015A268.

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Authors and Affiliations

  1. School of Electronic Engineering, Huainan Normal University, Huainan, 232038, People’s Republic of China

    Wen-Hai Zhang & Gang Ren

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  1. Wen-Hai Zhang
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  2. Gang Ren
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Correspondence to Wen-Hai Zhang.

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Zhang, WH., Ren, G. Unambiguous discrimination between linearly dependent equidistant states with multiple copies. Quantum Inf Process 17, 155 (2018). https://doi.org/10.1007/s11128-018-1929-3

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