Decay of Coherence and Entanglement of a Superposition State for a Continuous Variable System in an Arbitrary Heat Bath

TL;DR

This paper provides an exact analysis of how coherence and entanglement decay over time in a continuous variable quantum system interacting with an arbitrary heat bath, revealing that entanglement can abruptly disappear.

Contribution

It offers an exact calculation of the non-Gaussian state's evolution and demonstrates the occurrence of entanglement sudden death in continuous variable systems.

Findings

Coherence decays continuously over time.

Entanglement becomes zero at a finite time (entanglement sudden death).

Results are applicable to arbitrary heat baths.

Abstract

We consider the case of a pair of particles initially in a superposition state corresponding to a separated pair of wave packets. We calculate \emph{exactly} the time development of this non-Gaussian state due to interaction with an \emph{arbitrary} heat bath. We find that coherence decays continuously, as expected. We then investigate entanglement and find that at a finite time the system becomes separable (not entangled). Thus, we see that entanglement sudden death is also prevalent in continuous variable systems which should raise concern for the designers of entangled systems.