arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 0912.4252quant-ph
收藏

一种通向量子态空间的量子贝叶斯方法

A Quantum-Bayesian Route to Quantum-State Space

Christopher A. Fuchs, Ruediger Schack

摘要:

在量子基础的量子-贝叶斯方法中,量子态被看作是一个主体关于测量结果的个人主义贝叶斯置信度或概率的表达。这些概率服从荷兰书相干性所要求的通常概率规则,但量子力学对它们施加了额外的约束。在本文中,我们探讨的问题,推导出的量子态空间的结构从一组假设的精神,量子贝叶斯。出发点是由对称信息完全测量或SIC诱导的量子态的表示。在这种表示中,玻恩规则采取了对全概率定律的一种特别简单的修改形式。我们展示了如何从(i)玻恩定则作为全概率定律的简单修改和(ii)有限数量的强贝叶斯风味的附加假设中推导出量子态空间的关键特征。

英文摘要:

In the quantum-Bayesian approach to quantum foundations, a quantum state is viewed as an expression of an agent's personalist Bayesian degrees of belief, or probabilities, concerning the results of measurements. These probabilities obey the usual probability rules as required by Dutch-book coherence, but quantum mechanics imposes additional constraints upon them. In this paper, we explore the question of deriving the structure of quantum-state space from a set of assumptions in the spirit of quantum Bayesianism. The starting point is the representation of quantum states induced by a symmetric informationally complete measurement or SIC. In this representation, the Born rule takes the form of a particularly simple modification of the law of total probability. We show how to derive key features of quantum-state space from (i) the requirement that the Born rule arises as a simple modification of the law of total probability and (ii) a limited number of additional assumptions of a strong Bayesian flavor.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑