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<p>We show a connection between the minimax and Bayes approaches in quantum decision theory in a general setting of normal states on a von Neumann algebra. In particular, the quantum minimax theorem is proven in a fairly general situation, and it is shown that every minimax strategy is Bayes for some a priori distribution on the set of states—a so-called <i>least favourable prior</i>. Minimax strategies with constant risk are investigated in some detail. It turns out that in dimension greater than two such a strategy can be Bayes for a non-uniform a priori distribution which, at the same time, is a least favourable prior.</p>

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Quantum decision theory—minimax approach

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月23日

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  • Andrzej Łuczak

摘要

We show a connection between the minimax and Bayes approaches in quantum decision theory in a general setting of normal states on a von Neumann algebra. In particular, the quantum minimax theorem is proven in a fairly general situation, and it is shown that every minimax strategy is Bayes for some a priori distribution on the set of states—a so-called least favourable prior. Minimax strategies with constant risk are investigated in some detail. It turns out that in dimension greater than two such a strategy can be Bayes for a non-uniform a priori distribution which, at the same time, is a least favourable prior.