Chaotic Einstein-Podolsky-Rosen pairs, measurements and time reversal

TL;DR

This paper explores the reversibility of entangled EPR pairs evolving in quantum chaotic systems, showing that quantum effects preserve reversibility despite classical chaos, with implications for cold atom experiments.

Contribution

It demonstrates that quantum entanglement affects time reversal in chaotic systems, revealing that quantum dynamics remain reversible on short timescales even when classical chaos causes irreversibility.

Findings

Quantum evolution remains reversible on Ehrenfest timescale.

Measurement of one particle breaks time reversal of the entangled partner.

Experimental realization with cold atoms is feasible.

Abstract

We consider a situation when evolution of an entangled Einstein-Podolsky-Rosen (EPR) pair takes place in a regime of quantum chaos being chaotic in the classical limit. This situation is studied on an example of chaotic pair dynamics described by the quantum Chirikov standard map. The time evolution is reversible even if a presence of small errors breaks time reversal of classical dynamics due to exponential growth of errors induced by exponential chaos instability. However, the quantum evolution remains reversible since a quantum dynamics instability exists only on a logarithmically short Ehrenfest time scale. We show that due to EPR pair entanglement a measurement of one particle at the moment of time reversal breaks exact time reversal of another particle which demonstrates only an approximate time reversibility. This result is interpreted in the framework of the Schmidt decomposition and Feynman path integral formulation of quantum mechanics. The time reversal in this system has already been realized with cold atoms in kicked optical lattices in absence of entanglement and measurements. On the basis of the obtained results we argue that the experimental investigations of time reversal of chaotic EPR pairs is within reach of present cold atom capabilities.