共轭逻辑
Conjugate Logic
AI总结：
提出共轭逻辑以刻画量子和类量子系统行为，通过引入命题转换机制统一了稳定子量子力学与Spekkens玩具理论，为区分真正量子与类量子行为提供了新框架。
摘要：
我们提出了一种能够刻画量子和类量子系统行为的共轭逻辑。该提议类似于更广义的认识逻辑概念：它编码了关于某些系统未来观测结果的知识，或者更准确地说，预测。对于量子系统，这些预测是关于在系统的特定自由度上执行测量的未来结果的陈述。所提出的逻辑将包含命题及其关系（包括连接词），但重要的是，还包括系统共轭自由度上命题之间的转换。一个关键点是增加了一种转换，允许将关于单一系统的命题转换为关于系统间相关性的命题。我们将看到，对转换属性的微妙选择会导致截然不同的底层数学模型；一种选择给出稳定子量子力学，而另一种选择给出 Spekkens 的玩具理论。这指向了量子和类量子系统的一个关键基本属性，可以通过调整上述选择在当前的共轭逻辑中处理。它还使得讨论哪些行为是真正的量子行为或仅仅是类量子行为成为可能，这与该选择及其在被审查系统中的表现有关。
英文摘要：
We propose a conjugate logic that can capture the behavior of quantum and quantum-like systems. The proposal is similar to the more generic concept of epistemic logic: it encodes knowledge or perhaps more correctly, predictions about outcomes of future observations on some systems. For a quantum system, these predictions are statements about future outcomes of measurements performed on specific degrees of freedom of the system. The proposed logic will include propositions and their relations including connectives, but importantly also transformations between propositions on conjugate degrees of freedom of the systems. A key point is the addition of a transformation that allows to convert propositions about single systems into propositions about correlations between systems. We will see that subtle choices of the properties of the transformations lead to drastically different underlying mathematical models; one choice gives stabilizer quantum mechanics, while another choice gives Spekkens' toy theory. This points to a crucial basic property of quantum and quantum-like systems that can be handled within the present conjugate logic by adjusting the mentioned choice. It also enables a discussion on what behaviors are properly quantum or only quantum-like, relating to that choice and how it manifests in the system under scrutiny.
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