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We consider a situation when evolution of an entangledEinstein-Podolsky-Rosen (EPR) pair takes place in a regime of quantum chaosbeing chaotic in the classical limit. This situation is studied on an exampleof chaotic pair dynamics described by the quantum Chirikov standard map. Thetime evolution is reversible even if a presence of small errors breaks timereversal of classical dynamics due to exponential growth of errors induced byexponential chaos instability. However, the quantum evolution remainsreversible since a quantum dynamics instability exists only on alogarithmically short Ehrenfest time scale. We show that due to EPR pairentanglement a measurement of one particle at the moment of time reversalbreaks exact time reversal of another particle which demonstrates only anapproximate time reversibility. This result is interpreted in the framework ofthe Schmidt decomposition and Feynman path integral formulation of quantummechanics. The time reversal in this system has already been realized with coldatoms in kicked optical lattices in absence of entanglement and measurements.On the basis of the obtained results we argue that the experimentalinvestigations of time reversal of chaotic EPR pairs is within reach of presentcold atom capabilities.

the european physical journal. d, atomic, molecular and optical physics/the european physical journal. d, atomic, molecular, optical and plasma physics

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