Entangled quantum trajectories in relativistic systems

TL;DR

This paper develops a framework for analyzing entanglement in relativistic quantum systems using multi-time trajectories, addressing challenges in quantum communication across inertial frames.

Contribution

It introduces a novel approach to describe entangled quantum trajectories in relativistic settings, including new Euler--Lagrange equations under non-entangling constraints.

Findings

Derived equations for relativistic entangled trajectories

Quantified relativistic effects on quantum entanglement

Applied framework to Klein--Gordon particles

Abstract

Quantum entanglement is a key resource for quantum technologies, including emerging ground-to-satellite quantum communication. In such a scenario, an important challenge to be overcome is to consider entanglement between two or more quantum particles in different inertial frames, potentially experiencing relativistic effects affecting quantum correlations. In this paper, we present a consistent framework that overcomes this challenge. To this end, we establish the notion of factorizable and entangled multi-time trajectories and derive a class of Euler--Lagrange equations under the constraint of a non-entangling behavior. Comparing this restricted evolution to the solutions of the unrestricted equations of motion allows one to investigate the trajectory-based entanglement of general systems. We solve our equations for interacting particles in a Klein--Gordon-type setting, thereby quantifying the dynamic and relativistic impact of entanglement in a self-consistent manner.