重探量子因果结构的动力学——因果序何时可以演化？
Revisiting dynamics of quantum causal structures -- when can causal order evolve?
AI总结：
本文指出过程矩阵框架关于连续可逆变换必保持因果序的结论存在局限，并在标准量子力学框架下证明因果序可以演化，进而解释矛盾根源并给出调和方案。
摘要：
近来，人们对研究量子理论中超越状态的动力学产生了浓厚兴趣，特别是信道、测量和高阶变换的动力学。文献[Phys. Rev. X 8(1), 011047 (2018)]利用过程矩阵形式体系对此进行了研究，并给出了此类过程矩阵可能动力学的定义，尤其关注因果结构的演化问题。其主要结论之一是一个强定理：在该形式体系内，在连续且可逆的变换下，操作之间的因果序必须得到保持。我们在此的结果对文献[Phys. Rev. X 8(1), 011047 (2018)]的结论提出了挑战：如果在标准量子力学形式体系内考虑操作物理演化的完整图景，那么该文献的结论并不成立。也就是说，我们表明，在某些连续且可逆的动力学下，操作之间的因果序并不必然得到保持。此外，我们识别并分析了这一表面矛盾的根源，具体而言，被广泛接受并应用的高阶过程框架虽然在数学上是可靠的，但并不总是适合得出关于物理动力学的结论。最后，我们基于通过局部操作和经典通信处理纠缠的直觉，展示了如何调和整个图景中的各个要素。
英文摘要：
Recently, there has been substantial interest in studying the dynamics of quantum theory beyond that of states, in particular, the dynamics of channels, measurements, and higher-order transformations. Ref. [Phys. Rev. X 8(1), 011047 (2018)] pursues this using the process-matrix formalism, together with a definition of the possible dynamics of such process matrices, and focusing especially on the question of evolution of causal structures. One of its major conclusions is a strong theorem saying that within the formalism, under continuous and reversible transformations, the causal order between operations must be preserved. Our result here challenges that of Ref. [Phys. Rev. X 8(1), 011047 (2018)]: if one is to take into account a full picture of the physical evolution of operations within the standard quantum-mechanical formalism, then the conclusion of Ref. [Phys. Rev. X 8(1), 011047 (2018)] does not hold. That is, we show that under certain continuous and reversible dynamics, the causal order between operations is not necessarily preserved. We moreover identify and analyse the root of this apparent contradiction, specifically, that the commonly accepted and widely applied framework of higher-order processes, whilst mathematically sound, is not always appropriate for drawing conclusions on physical dynamics. Finally, we show how to reconcile the elements of the whole picture following the intuition based on entanglement processing by local operations and classical communication.
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