量子决策理论-极小极大方法

IF 2.2 3区物理与天体物理 Q1 PHYSICS, MATHEMATICAL

Quantum Information Processing Pub Date : 2025-09-23 DOI:10.1007/s11128-025-04924-1

Andrzej Łuczak

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引用次数: 0

摘要

我们展示了量子决策理论中最小极大和贝叶斯方法在冯·诺伊曼代数上的一般正常状态设置之间的联系。特别地，量子极大极小定理在相当一般的情况下得到了证明，并且证明了对于状态集上的某个先验分布（所谓的最不利先验），每个极大极小策略都是贝叶斯。对具有恒定风险的极大极小策略进行了详细的研究。事实证明，在大于2维的情况下，这种策略对于非均匀先验分布来说是贝叶斯的，同时也是最不利的先验。

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Quantum decision theory—minimax approach

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.

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来源期刊

Quantum Information Processing 物理-物理：数学物理

CiteScore

4.10

自引率

20.00%

发文量

337

审稿时长

4.5 months

期刊介绍： Quantum Information Processing is a high-impact, international journal publishing cutting-edge experimental and theoretical research in all areas of Quantum Information Science. Topics of interest include quantum cryptography and communications, entanglement and discord, quantum algorithms, quantum error correction and fault tolerance, quantum computer science, quantum imaging and sensing, and experimental platforms for quantum information. Quantum Information Processing supports and inspires research by providing a comprehensive peer review process, and broadcasting high quality results in a range of formats. These include original papers, letters, broadly focused perspectives, comprehensive review articles, book reviews, and special topical issues. The journal is particularly interested in papers detailing and demonstrating quantum information protocols for cryptography, communications, computation, and sensing.