用决策论解释量子不确定性，推导出波函数概率规则的合理性。
A decision-theoretic approach to dealing with uncertainty in quantum mechanics
- 将测量视为结果不确定的决策行为，构建基于效用函数的量子决策框架。
- 在已知量子态下，通过效用函数自然导出玻恩规则的概率分布。
- 支持模糊概率理论，为量子不确定性提供更普适的数学基础，适合理论物理与哲学研究者。
我们提出一种决策论框架来处理量子力学中的不确定性。这种不确定性具有双重性：一方面是对系统所处状态的不确定性；另一方面，即使量子态已知，测量仍可能产生不确定结果。在该框架中，测量被视为具有不确定结果的决策行为，其效用函数满足简单的决策公理，从而自然包含玻恩规则。该方法使精确概率论与量子力学解耦，为更一般的模糊概率理论留下空间。我们讨论了该发现的数学含义，为Benavoli、Facchini和Zaffalon的近期重要工作提供了决策论基础，并与Deutsch和Wallace的早期不同方法进行了比较。
原文摘要 · Abstract (English)
We provide a decision-theoretic framework for dealing with uncertainty in quantum mechanics. This uncertainty is two-fold: on the one hand there may be uncertainty about the state the quantum system is in, and on the other hand, as is essential to quantum mechanical uncertainty, even if the quantum state is known, measurements may still produce an uncertain outcome. In our framework, measurements therefore play the role of acts with an uncertain outcome and our simple decision-theoretic postulates ensure that Born's rule is encapsulated in the utility functions associated with such acts. This approach allows us to uncouple (precise) probability theory from quantum mechanics, in the sense that it leaves room for a more general, so-called imprecise probabilities approach. We discuss the mathematical implications of our findings, which allow us to give a decision-theoretic foundation to recent seminal work by Benavoli, Facchini and Zaffalon, and we compare our approach to earlier and different approaches by Deutsch and Wallace.
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