量子物理中的决策理论与信息传播
Decision theory and information propagation in quantum physics
摘要：
在最近的论文中，祖雷克反对多伊奇和华莱士推导量子概率玻恩定则的决策论方法，理由是它追求循环性。Deutsch和Wallace假设多世界理论是正确的，退相干产生了一个优选的基础。然而，退相干参数使用约化的密度矩阵，其依赖于部分迹线，因此依赖于玻恩法则的有效性。使用海森堡图像和量子达尔文主义-经典信息是量子信息的概念，可以在奥利弗等人开创的环境中增殖-我表明，两个系统之间的测量相互作用只创建一个特定的一组交换可观的系统1和一个特定的一组交换可观的系统2之间的相关性。这一论点指出了一个独特的基础，在这个基础上，信息在这些可交换的可观测量之间的相关性中流动。然后，我推导出纯态和混合态的玻恩规则，并回答了其他一些对量子概率决策论方法的批评。
英文摘要：
In recent papers, Zurek has objected to the decision-theoretic approach of Deutsch and Wallace to deriving the Born rule for quantum probabilities on the grounds that it courts circularity. Deutsch and Wallace assume that the many worlds theory is true and that decoherence gives rise to a preferred basis. However, decoherence arguments use the reduced density matrix, which relies upon the partial trace and hence upon the Born Rule for its validity. Using the Heisenberg Picture and quantum Darwinism - the notion that classical information is quantum information that can proliferate in the environment pioneered by Olliver et al - I show that measurement interactions between two systems only create correlations between a specific set of commuting observables of system 1 and a specific set of commuting observables of system 2. This argument picks out a unique basis in which information flows in the correlations between those sets of commuting observables. I then derive the Born rule for both pure and mixed states and answer some other criticisms of the decision theoretic approach to quantum probability.
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