Relativistic three-partite non-locality

TL;DR

This paper investigates how relativistic effects influence three-particle non-locality, showing that non-local correlations diminish with increasing velocity and vanish at the speed of light, using Svetlichny's inequality and Czachor's spin operator.

Contribution

It demonstrates the relativistic behavior of three-particle non-locality for GHZ and W states, highlighting the velocity-independent nature of Svetlichny's inequality satisfaction in the ultra-relativistic limit.

Findings

Maximal violation of Svetlichny's inequality decreases with velocity.

Non-locality vanishes as velocity approaches the speed of light.

Results are consistent across different three-particle states and configurations.

Abstract

Bell-like inequalities have been used in order to distinguish non-local quantum pure states by various authors. The behavior of such inequalities under Lorentz transformation has been a source of debate and controversies in the past. In this paper, we consider the two most commonly studied three-particle pure states, that of W and GHZ states which exhibit distinctly different type of entanglement. We discuss the various types of three-particle inequalities used in previous studies and point to their corresponding shortcomings and strengths. Our main result is that if one uses Czachor's relativistic spin operator and Svetlichny's inequality as the main measure of non-locality and uses the same angles in the rest frame ($S$) as well as the moving frame ($S^{\prime}$), then maximally violated inequality in $S$ will decrease in the moving frame, and will eventually lead to lack of non-locality ( i.e. satisfaction of inequality) in the $v \rightarrow c$ limit. This is shown for both the GHZ and W states and in two different configurations which are commonly studied (\textbf{Case $I$} and \textbf{Case $II$}). Our results are in line with a more familiar case of two particle case. We also show that the satisfaction of Svetlichny's inequality in the $v\rightarrow c$ limit is independent of initial particles' velocity. Our study shows that whenever we use Czachor's relativistic spin operator, results draws a clear picture of three-particle non-locality making its general properties consistent with previous studies on two-particle systems regardless of the W state or the GHZ state is involved.....