Sanz Ángel S
Department of Optics, Faculty of Physical Sciences, Universidad Complutense de Madrid, Pza. Ciencias 1, Ciudad Universitaria, 28040 Madrid, Spain.
Entropy (Basel). 2022 Jan 27;24(2):190. doi: 10.3390/e24020190.
The correspondence principle plays a fundamental role in quantum mechanics, which naturally leads us to inquire whether it is possible to find or determine close classical analogs of quantum states in phase space-a common meeting point to both classical and quantum density statistical descriptors. Here, this issue is tackled by investigating the behavior of classical analogs arising upon the removal of all interference traits displayed by the Wigner distribution functions associated with a given pure quantum state. Accordingly, the dynamical evolution of the linear and von Neumann entropies is numerically computed for a continuous-variable bipartite system, and compared with the corresponding classical counterparts, in the case of two quartic oscillators nonlinearly coupled under regular and chaos conditions. Three quantum states for the full system are considered: a Gaussian state, a cat state, and a Bell-type state. By comparing the quantum and classical entropy values, and particularly their trends, it is shown that, instead of entanglement production, such entropies rather provide us with information on the system (either quantum or classical) delocalization. This gradual loss of information translates into an increase in both the quantum and the classical realms, directly connected to the increase in the correlations between both parties' degrees of freedom which, in the quantum case, is commonly related to the production of entanglement.
对应原理在量子力学中起着基础性作用，这自然促使我们去探究是否有可能在相空间中找到或确定量子态的近似经典类似物——这是经典和量子密度统计描述符的一个共同交汇点。在此，通过研究去除与给定纯量子态相关的维格纳分布函数所显示的所有干涉特征后产生的经典类似物的行为来解决这个问题。相应地，对于一个连续变量的两体系统，数值计算了线性熵和冯·诺依曼熵的动力学演化，并在两个四次方振子在规则和混沌条件下非线性耦合的情况下，与相应的经典对应物进行了比较。考虑了全系统的三种量子态：一个高斯态、一个猫态和一个贝尔型态。通过比较量子熵和经典熵的值，特别是它们的趋势，结果表明，这些熵并非提供纠缠产生的信息，而是为我们提供了关于系统（量子或经典）离域化的信息。这种信息的逐渐丢失转化为量子和经典领域中熵的增加，这直接与双方自由度之间相关性的增加相关，在量子情况下，这种相关性通常与纠缠的产生有关。
