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arXiv · 1601.06231

Upper and Lower Bounds on Optimal Success Probability of Quantum State Discrimination with and without Inconclusive Results

Kenji Nakahira·Tsuyoshi Sasaki Usuda·Kentaro Kato
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Abstract

We propose upper and lower bounds on the maximum success probability for discriminating given quantum states. The proposed upper bound is obtained from a suboptimal solution to the dual problem of the corresponding optimal state discrimination problem. We also give a necessary and sufficient condition for the upper bound to achieve the maximum success probability; the proposed lower bound can be obtained from this condition. It is derived that a slightly modified version of the proposed upper bound is tighter than that proposed by Qiu et al. [Phys. Rev. A 81, 042329 (2010)]. Moreover, we propose upper and lower bounds on the maximum success probability with a fixed rate of inconclusive results. The performance of the proposed bounds are evaluated through numerical experiments.

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Kenji Nakahira, Tsuyoshi Sasaki Usuda, Kentaro Kato. 2016-01-23. Upper and Lower Bounds on Optimal Success Probability of Quantum State Discrimination with and without Inconclusive Results. https://doi.org/10.1103/physreva.97.012103

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