对测量结果的打赌：量子概率的贝叶斯理论

Betting on Quantum Objects

Dutch book arguments have been applied to beliefs about the outcomes of measurements of quantum systems, but not to beliefs about quantum objects prior to measurement. In this paper, we prove a quantum version of the probabilists' Dutch book theorem that applies to both sorts of beliefs: roughly, if ideal beliefs are given by vector states, all and only Born-rule probabilities avoid Dutch books. This theorem and associated results have implications for operational and realist interpretations of the logic of a Hilbert lattice. In the latter case, we show that the defenders of the eigenstate-val…

Kelly Betting with Quantum Payoff: a continuous variable approach

The main purpose of this study is to introduce a semi-classical model describing betting scenarios in which, at variance with conventional approaches, the payoff of the gambler is encoded into the internal degrees of freedom of a quantum memory element. In our scheme, we assume that the invested capital is explicitly associated with the quantum analog of the free-energy (i.e. ergotropy functional by Allahverdyan, Balian, and Nieuwenhuizen) of a single mode of the electromagnetic radiation which, depending on the outcome of the betting, experiences attenuation or amplification processes which m…

Social optimality in quantum Bayesian games

A significant aspect of the study of quantum strategies is the exploration of the game-theoretic solution concept of the Nash equilibrium in relation to the quantization of a game. Pareto optimality is a refinement on the set of Nash equilibria. A refinement on the set of Pareto optimal outcomes is known as social optimality in which the sum of players' payoffs are maximized. This paper analyzes social optimality in a Bayesian game that uses the setting of generalized Einstein-Podolsky-Rosen experiments for its physical implementation. We show that for the quantum Bayesian game a direct connec…

量子层析成像的自适应贝叶斯和频率论数据处理

Adaptive Bayesian and frequentist data processing for quantum tomography

对于给定状态下的系统，信息上完全的量子测量的结果统计可以用于通过对取决于特定算子的结果的函数求平均来评估相同状态下的任何线性算子的系综期望。在这里，我们介绍了两种新的数据处理策略，非线性的频率，导致更快的收敛到理论预期。

量子贝叶斯相干

Quantum-Bayesian Coherence

在量子量子力学理论中，玻恩规则不能被解释为一个从客观量子态设定测量结果概率的规则。如果不是，规则的作用是什么？在本文中，我们认为，它应该被视为一个经验除了贝叶斯推理本身。特别是，我们将展示如何看待出生规则作为一个规范性的规则，除了通常的荷兰书的连贯性。这是一个规则，考虑到人们应该如何分配概率的结果，各种预期的测量对物理系统，但明确的先验概率和条件概率后，想象的结果，一个特殊的反事实的参考测量。通过用固定的、基准对称信息完备（SIC）测量结果的概率来表示量子态，可以特别清楚地看到这种解释。我们进一步探讨了新规范规则的一般形式在多大程度上隐含了量子力学的完整态空间结构。似乎已经走得很远了。

量子双倍或全无博弈：自旋的凯利准则

A quantum double-or-nothing game: The Kelly Criterion for Spins

本文提出一种基于自旋1/2粒子的双倍或全无量子博弈，通过数值方法确定最优量子策略，证明其不同于经典凯利准则，推动量子金融发展。