Temporal and Spatial Dependence of Quantum Entanglement from a Field Theory Perspective

TL;DR

This paper investigates how quantum entanglement between two detectors depends on their spatial separation and causal contact, revealing oscillations, interference effects, and conditions for entanglement persistence or creation within a quantum field theory framework.

Contribution

It provides a detailed quantum field theory analysis of entanglement dynamics, highlighting spatial and causal influences on entanglement behavior between detectors.

Findings

Entanglement oscillates when detectors are outside each other's light cone.

Stronger relative entanglement correlates with longer disentanglement times.

No entanglement creation outside the light cone for initially separable states.

Abstract

We consider the entanglement dynamics between two Unruh-DeWitt detectors at rest separated at a distance $d$. This simple model when analyzed properly in quantum field theory shows many interesting facets and helps to dispel some misunderstandings of entanglement dynamics. We find that there is spatial dependence of quantum entanglement in the stable regime due to the phase difference of vacuum fluctuations the two detectors experience, together with the interference of the mutual influences from the backreaction of one detector on the other. When two initially entangled detectors are still outside each other's light cone, the entanglement oscillates in time with an amplitude dependent on spatial separation $d$. When the two detectors begin to have causal contact, an interference pattern of the relative degree of entanglement (compared to those at spatial infinity) develops a parametric dependence on $d$. The detectors separated at those $d$ with a stronger relative degree of entanglement enjoy longer disentanglement times. In the cases with weak coupling and large separation, the detectors always disentangle at late times. For sufficiently small $d$, the two detectors can have residual entanglement even if they initially were in a separable state, while for $d$ a little larger, there could be transient entanglement created by mutual influences. However, we see no evidence of entanglement creation outside the light cone for initially separable states.