Genuine Multipartite Nonlocality sharing under sequential measurement

TL;DR

This paper investigates how genuine multipartite nonlocality can be shared among multiple observers in $n$-qubit GHZ states using unbiased unsharp measurements, revealing limits on sharing in both unilateral and multilateral scenarios.

Contribution

It extends nonlocality sharing analysis to $n$-qubit GHZ states under sequential measurements, providing new bounds and strategies for sharing nonlocality.

Findings

Maximum two copies of an observer can share nonlocality in four-qubit GHZ state

Multilateral sharing does not surpass unilateral sharing in the studied scenarios

Unsharp measurements are crucial for optimizing nonlocality sharing

Abstract

The study of quantum nonlocality sharing has garnered significant attention, particularly for two-qubit and three-qubit entangled systems. In this paper, we extend the investigation to $n$-qubit Greenberger-Horne-Zeilinger (GHZ) systems, analyzing nonlocality sharing under unbiased unsharp measurements. Employing the Seevink and Svetlichny inequalities, we explore both unilateral and multilateral sequential measurement scenarios. In the unilateral scenario, we derive the range for which an observer's multiple copies can share genuine $n$-partite nonlocality with single copies of the remaining parties. In the multilateral scenario, we identify the maximum number of independent observers on $m$ sides who can share genuine $n$-partite nonlocality with other parties. A crucial aspect of our results is that all findings stem from a measurement strategy where each sequential observer utilizes unbiased unsharp measurements. As a specific case, for the four-qubit maximally entangled GHZ state, we demonstrate that at most two copies of an observer (e.g., Alice) can share nonlocality in the unilateral sequential measurement scenario. However, in the multilateral scenario, no additional sharing is possible compared to the unilateral case. This finding highlights the significance of unsharp measurements in optimizing the recycling of qubits for generating quantum nonlocality.