Relativity of quantum states in entanglement swapping: Violation of Bell's inequality with no entanglement

TL;DR

This paper investigates how relativistic effects influence entanglement swapping and Bell inequality violations, revealing that entanglement and Bell violations can appear differently in various frames, even without actual entanglement.

Contribution

It demonstrates that relativistic frames can alter the perceived entanglement and Bell violations, highlighting the relativity of quantum states and the non-local, non-simultaneous nature of entanglement.

Findings

Bell violation observed without entanglement in a moving frame

Wavefunctions differ between frames despite identical measurement results

Maximum Bell violation can occur across non-simultaneous points with decoherence

Abstract

The entanglement swapping protocol is analyzed in a relativistic setting, where shortly after the entanglement swapping is performed, a Bell violation measurement is performed. From an observer in the laboratory frame, a Bell violation is observed due to entanglement swapping taking place, but in a moving frame the order of the measurements is reversed, and a Bell violation is observed even though no entanglement is present. Although the measurement results are identical, the wavefunctions for the two frames are different--- one is entangled and the other is not. Furthermore, for boosts in a perpendicular direction, in the presence of decoherence, we show that a maximum Bell violation can occur across non-simultaneous points in time. This is a signature of entanglement that is spread across both space and time, showing both the non-local and non-simultaneous feature of entanglement.