Quantum-classical entropy analysis for nonlinearly-coupled continuous-variable bipartite systems

TL;DR

This paper investigates the relationship between quantum and classical entropy in nonlinearly coupled continuous-variable bipartite systems, revealing that entropy trends reflect system delocalization rather than entanglement, across regular and chaotic regimes.

Contribution

It introduces a method to compare quantum and classical entropies in bipartite systems, highlighting entropy's role in indicating delocalization over entanglement.

Findings

Quantum and classical entropies increase with system delocalization.

Entropy trends are similar in quantum and classical regimes, regardless of chaos.

Entropies reflect correlations and delocalization, not just entanglement.

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.