Abstract
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.
Highlights
Academic Editor: Rosario Lo FrancoEntanglement can be regarded as the characteristic trait of quantum mechanics, recalling Schrödinger [1], which means it plays a central role, as an essential resource, in the implementation and development of modern quantum technologies [2,3]
Due to its connection to chaotic dynamics, this model has been extensively studied in the literature both classically [51–53] and quantum mechanically [53–56]
With the purpose to compare on equal footing, and to determine whether any quantum–classical correspondence can be established, two coupled continuous-variable bipartite systems have been considered, consisting of two one-dimensional quartic oscillators nonlinearly coupled by means of a biquadratic term, which has been shown to display either regular or chaotic dynamics depending on the coupling strength
Summary
Academic Editor: Rosario Lo FrancoEntanglement can be regarded as the characteristic trait of quantum mechanics, recalling Schrödinger [1], which means it plays a central role, as an essential resource, in the implementation and development of modern quantum technologies [2,3]. The capability to transfer information at long distances between two entangled parties without a physical interaction mediating between them [1,4] sets a crucial difference with respect to two classically correlated systems, where information transmission necessarily requires the active action of physical interactions. This is consistent with the common statement that there is no classical analog for entanglement. This seems in contradiction with the fact that, by virtue of the correspondence principle, classical mechanics should approximate quantum mechanics in one way or another, or, at least, manifest in some form. It has been found that the amount of entanglement increases in rates proportional to the corresponding
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