Ciaglia Florio M, Di Cosmo Fabio, Ibort Alberto, Marmo Giuseppe
Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany.
ICMAT, Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), Nicolás Cabrera, 13-15, Campus de Cantoblanco, UAM, 28049 Madrid, Spain.
Entropy (Basel). 2020 Nov 13;22(11):1292. doi: 10.3390/e22111292.
The evolution of states of the composition of classical and quantum systems in the groupoid formalism for physical theories introduced recently is discussed. It is shown that the notion of a classical system, in the sense of Birkhoff and von Neumann, is equivalent, in the case of systems with a countable number of outputs, to a totally disconnected groupoid with Abelian von Neumann algebra. The impossibility of evolving a separable state of a composite system made up of a classical and a quantum one into an entangled state by means of a unitary evolution is proven in accordance with Raggio's theorem, which is extended to include a new family of separable states corresponding to the composition of a system with a totally disconnected space of outcomes and a quantum one.
讨论了最近引入的物理理论的广群形式体系中经典和量子系统组成状态的演化。结果表明，在具有可数数量输出的系统情况下，伯克霍夫和冯·诺依曼意义下的经典系统概念等同于具有阿贝尔冯·诺依曼代数的完全不连通广群。根据拉吉奥定理证明了由经典和量子系统组成的复合系统的可分态不可能通过酉演化演化为纠缠态，该定理被扩展以包括对应于具有完全不连通结果空间的系统与量子系统组成的新的可分态族。
