How the relativistic motion affects Einstein-Podolsky-Rosen steering

TL;DR

This paper investigates how relativistic effects, specifically the Unruh effect, influence EPR steering, revealing its destruction, asymmetry, and redistribution in non-inertial frames, with implications for quantum communication.

Contribution

It provides the first analysis of EPR steering behavior under relativistic acceleration, highlighting its unique properties and potential for quantum communication in relativistic settings.

Findings

EPR steering from Alice to Bob is dramatically destroyed by the Unruh effect.

EPR steering asymmetry increases with acceleration, influenced by the Unruh effect.

Only one EPR steering direction experiences a sudden birth with increasing acceleration.

Abstract

In this Letter, the dynamic behavior of Einstein-Podolsky-Rosen (EPR) steering and the redistribution of EPR steering under a relativistic framework are investigated. Specifically, we explore the scenario that particle A hold by Alice is in a flat space-time and another particle B by Bob entangled with A is in a non-inertial framework. The results show that EPR steering from Alice to Bob is dramatically destroyed by Unruh effect caused by the acceleration of Bob. Besides, EPR steering has an asymmetry property, and EPR steering asymmetry increases with the growing intensity of Unruh effect, implying that the Unruh effect can bring on EPR steering asymmetry. Furthermore, the reduced physical accessible EPR steering from Alice to Bob is distributed to the physical inaccessible EPR steering (from Alice to anti-Bob or from Bob to anti-Bob). Notably, unlike entanglement and quantum discord, only one of EPR steering from Alice to anti-Bob and Bob to anti-Bob experiences a sudden birth with the increase of acceleration parameter, which means that they cannot simultaneously survive. That is, the monogamy relation of EPR steering is still tenable in such a scenario. Consequently, we believe that EPR steering could also be served as one of important information resources within the long-distance quantum secure communication under the relativistic framework.