AI 中文总结
本文将无信号条件推广到动力学情形，研究其对经典-量子相互作用的影响，发现该条件等价于概率测度变换的凸线性，且约束了经典与量子自由度的相互作用方式。
AI 中文摘要
混合经典-量子方法在从凝聚态物理到量子信息科学的众多领域中发挥着重要作用。我们最近提出，可通过一组针对测量概率的自然公理来描述混合系统，无需添加任何底层数学结构。由此定义的概率测度满足无信号条件，该条件确保瞬时通信不可能实现。本文中我们对该条件进行动力学推广，其含义是：对于两个独立系统，对其中一个系统进行测量的结果概率，不会受到此前对另一个系统所做测量的影响。通常的经典和量子双partite系统满足类似要求，若违反这些要求则可能实现超光速信号传递。动力学无信号条件对经典-量子相互作用具有重要影响，具体取决于所使用的混合方法。对于具有经典轨迹的无信号混合动力学，经典自由度可以影响量子自由度，但后者无法对前者产生反作用。若量子系统的纯态保持纯态，则动力学无信号条件意味着不存在经典反作用。当允许所有混合态时，对于不产生经典与量子自由度之间关联的无信号混合动力学，不存在真正的经典-量子相互作用。在所有这些情况下，所提出的条件等价于描述有限时间演化的概率测度变换的凸线性。
英文摘要
Hybrid classical-quantum approaches are instrumental in numerous fields, from condensed matter physics to quantum information science. We recently proposed to describe hybrid systems starting from a set of natural axioms for measurement probabilities without adding any underlying mathematical structure. The so defined probability measures fulfill a no-signaling condition that ensures that instantaneous communication is impossible. We formulate here a dynamical generalization of this condition. It means that, for two independent systems, the outcome probabilities of a measurement made on one of them are not affected by a measurement performed earlier on the other. Analogous requirements are satisfied for usual classical and quantum bipartite systems and violating them would make faster-than-light signaling possible. The dynamical no-signaling condition has important consequences for classical-quantum interactions that depend on the hybrid approach used. For no-signaling hybrid dynamics with classical trajectories, the classical degrees of freedom can influence the quantum ones but the latter cannot react on the former. If pure states of quantum systems remain pure then the dynamical no-signaling condition implies the absence of classical reaction. When all hybrid states are allowed, there are no genuine classical-quantum interactions for no-signaling hybrid dynamics that do not generate correlations between the classical and the quantum degrees of freedom. In all these cases, the proposed condition is equivalent to the convex-linearity of the probability measure transformations describing finite-time evolutions.
