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Uniqueness of Minimax Strategy in View of Minimum Error Discrimination of Two Quantum States

Department of Applied Physics, Hanyang University, Ansan, Kyunggi-Do 425-791, Korea
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Entropy 2019, 21(7), 671; https://doi.org/10.3390/e21070671
Received: 28 May 2019 / Revised: 4 July 2019 / Accepted: 6 July 2019 / Published: 9 July 2019
(This article belongs to the Special Issue Entropy in Foundations of Quantum Physics)
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Abstract

This study considers the minimum error discrimination of two quantum states in terms of a two-party zero-sum game, whose optimal strategy is a minimax strategy. A minimax strategy is one in which a sender chooses a strategy for a receiver so that the receiver may obtain the minimum information about quantum states, but the receiver performs an optimal measurement to obtain guessing probability for the quantum ensemble prepared by the sender. Therefore, knowing whether the optimal strategy of the game is unique is essential. This is because there is no alternative if the optimal strategy is unique. This paper proposes the necessary and sufficient condition for an optimal strategy of the sender to be unique. Also, we investigate the quantum states that exhibit the minimum guessing probability when a sender’s minimax strategy is unique. Furthermore, we show that a sender’s minimax strategy and a receiver’s minimum error strategy cannot be unique if one can simultaneously diagonalize two quantum states, with the optimal measurement of the minimax strategy. This implies that a sender can confirm that the optimal strategy of only a single side (a sender or a receiver but not both of them) is unique by preparing specific quantum states. View Full-Text
Keywords: quantum state discrimination; quantum minimax; uniqueness of strategy; guessing probability quantum state discrimination; quantum minimax; uniqueness of strategy; guessing probability
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Kim, J.; Ha, D.; Kwon, Y. Uniqueness of Minimax Strategy in View of Minimum Error Discrimination of Two Quantum States. Entropy 2019, 21, 671.

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