"Hot Entanglement"? -- A Nonequilibrium Quantum Field Theory Scrutiny

TL;DR

This paper investigates whether quantum entanglement can be maintained at high temperatures by analyzing a model of two coupled oscillators in a thermal bath, concluding that hot entanglement is unlikely due to thermal effects.

Contribution

It provides a nonequilibrium quantum field theory analysis showing the limitations of sustaining entanglement at high temperatures in a specific oscillator-bath model.

Findings

Coupling enhances entanglement at intermediate temperatures.

Field-induced interactions are ineffective at high temperatures.

Critical temperature for entanglement is bounded by oscillator frequency.

Abstract

The possibility of maintaining entanglement in a quantum system at finite, even high, temperatures -- the so-called `hot entanglement' -- has obvious practical interest, but also requires closer theoretical scrutiny. Since quantum entanglement in a system evolves in time and is continuously subjected to environmental degradation, a nonequilibrium description by way of open quantum systems is called for. To identify the key issues and the contributing factors that may permit `hot entanglement' to exist, or the lack thereof, we carry out a model study of two spatially-separated, coupled oscillators in a shared bath depicted by a finite-temperature scalar field. From the Langevin equations we derived for the normal modes and the entanglement measure constructed from the covariance matrix we examine the interplay between direct coupling, field-induced interaction and finite separation on the structure of late-time entanglement. We show that the coupling between oscillators plays a crucial role in sustaining entanglement at intermediate temperatures and over finite separations. In contrast, the field-induced interaction between the oscillators which is a non-Markovian effect, becomes very ineffective at high temperature. We determine the critical temperature above which entanglement disappears to be bounded in the leading order by the inverse frequency of the center-of-mass mode of the reduced oscillator system, a result not unexpected, which rules out hot entanglement in such settings.