论文标题
除了分类量子力学中的纯度和混合物之外
Beyond Purity and Mixtures in Categorical Quantum Mechanics
论文作者
论文摘要
在最近的一篇论文[12]中，我们讨论了纯状态概念的操作和数学定义中存在的严重不一致。继续进行这项分析，在这项工作中，我们试图解决“纯度”和“混合物”在QM的两种不同的分类方法中的作用，即，Chris Isham和Jeremy Butterfield [27，28，29]最初提出的Topos方法和本文[10，11，13]的作者提出的最新徽标分类方法。虽然第一种方法暴露了对纯状态和混合物的一致理解的困难，但后一种方法提出了一种新的方案，在该方案中，从一开始就将其参考被删除，而有利于对投影算子和量子叠加的深入了解。该理论的这一新叙述是基于对天生规则的密集解释的，不仅使我们不仅避免对投射操作员的正统解释，而且还避免了确定的有价值的属性或测量结果 - 还可以考虑在同等基础上（任何等级）的所有矩阵。从后一个角度来看，我们得出的结论是，与其区分纯状态和混合状态，不如说是对量子理论的适当理解 - 返回Werner Heisenberg在1925年提出的量子力学的原始矩阵公式。
In a recent paper [12], we discussed the serious inconsistency present within the operational and mathematical definition(s) of the notion of pure state. Continuing this analysis, in this work we attempt to address the role of 'purity' and 'mixtures' within two different categorical approaches to QM, namely, the topos approach originally presented by Chris Isham and Jeremy Butterfield [27, 28, 29] and the more recent logos categorical approach presented by the authors of this article [10, 11, 13]. While the first approach exposes the difficulties to produce a consistent understanding of pure states and mixtures, the latter approach presents a new scheme in which their reference is erased right from the start in favor of an intensive understanding of projection operators and quantum superpositions. This new account of the theory, grounded on an intensive interpretation of the Born rule, allows us not only to avoid the orthodox interpretation of projection operators --either as referring to definite valued properties or measurement outcomes-- but also to consider all matrices (of any rank) on equal footing. It is from this latter standpoint that we conclude that instead of distinguishing between pure and mixed states it would be recommendable --for a proper understanding of the theory of quanta-- to return to the original matrix formulation of quantum mechanics presented by Werner Heisenberg in 1925.
