未知量子态与量子运算的贝叶斯观点
Unknown Quantum States and Operations, a Bayesian View
摘要：
经典的de Finetti定理提供了贝叶斯概率论中未知概率概念的操作定义，其中概率被视为置信度而不是客观的自然状态。在本文中，我们动机和审查的两个结果，推广de Finetti定理的量子力学设置：即一个de Finetti定理的量子态和de Finetti定理的量子操作。量子态定理，在一个非常类似的方式，原来的德Finetti定理，处理可交换的密度算子分配，并提供了一个操作定义的概念，“未知的量子态“在量子态层析成像。类似地，量子操作定理给出了量子过程层析成像中“未知量子操作”的操作定义。这些结果对于量子力学的贝叶斯解释尤其重要，在贝叶斯解释中，量子态和（至少一些）量子操作被视为信念状态而不是自然状态。
英文摘要：
The classical de Finetti theorem provides an operational definition of the concept of an unknown probability in Bayesian probability theory, where probabilities are taken to be degrees of belief instead of objective states of nature. In this paper, we motivate and review two results that generalize de Finetti's theorem to the quantum mechanical setting: Namely a de Finetti theorem for quantum states and a de Finetti theorem for quantum operations. The quantum-state theorem, in a closely analogous fashion to the original de Finetti theorem, deals with exchangeable density-operator assignments and provides an operational definition of the concept of an "unknown quantum state" in quantum-state tomography. Similarly, the quantum-operation theorem gives an operational definition of an "unknown quantum operation" in quantum-process tomography. These results are especially important for a Bayesian interpretation of quantum mechanics, where quantum states and (at least some) quantum operations are taken to be states of belief rather than states of nature.
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