Spin Fidelity for Three-qubit Greenberger-Horne-Zeilinger and W States Under Lorentz Transformations

TL;DR

This paper investigates how Lorentz boosts affect the fidelity of three-qubit GHZ and W states' spin parts, revealing that increased boost speeds reduce fidelity to a non-zero limit influenced by momentum entanglement.

Contribution

It provides a numerical analysis of spin fidelity under Lorentz transformations for three-qubit states with Gaussian momentum distributions, highlighting the impact of boost speed and momentum entanglement.

Findings

Spin fidelity decreases with increasing boost speed.

Fidelity approaches a non-zero asymptotic value.

Asymptotic fidelity depends on momentum distribution and entanglement.

Abstract

Constructing the reduced density matrix for a system of three massive spin$-\frac{1}{2}$ particles described by a wave packet with Gaussian momentum distribution and a spin part in the form of GHZ or W state, the fidelity for the spin part of the system is investigated from the viewpoint of moving observers in the jargon of special relativity. Using a numerical approach, it turns out that by increasing the boost speed, the spin fidelity decreases and reaches to a non-zero asymptotic value that depends on the momentum distribution and the amount of momentum entanglement.