Trade-off relation among genuine three-qubit nonlocalities in four-qubit systems

TL;DR

This paper investigates the interdependent nature of genuine three-qubit nonlocalities within four-qubit systems, revealing a trade-off relation among Svetlichny operator mean values in reduced states of GHZ and W states.

Contribution

It introduces a novel trade-off relation among three-qubit nonlocalities in four-qubit systems, providing tighter bounds than previous individual bounds.

Findings

Existence of a trade-off relation among three-qubit nonlocalities.

Derived an upper bound for the sum of Svetlichny operator mean values.

Illustrated the relation with detailed examples.

Abstract

We study the trade-off relations satisfied by the genuine tripartite nonlocality in multipartite quantum systems. From the reduced three-qubit density matrices of the four-qubit generalized Greenberger-Horne-Zeilinger (GHZ) states and W states (4-qubit entangled state), we find that there exists a trade-off relation among the mean values of the Svetlichny operators associated with these reduced states. Namely, the genuine three-qubit nonlocalities are not independent. For four-qubit generalized GHZ states and W states, the summation of all their three-qubit maximal (squared) mean values of the Svetlichny operator has an upper bound. This bound is better than the one derived from the upper bounds of individual three-qubit mean values of the Svetlichny operator. Detailed examples are presented to illustrate the trade-off relation among the three-qubit nonlocalities.