Achievable Trade-Off in Network Nonlocality Sharing

TL;DR

This paper investigates the fundamental limits and trade-offs in sharing quantum nonlocality across networks, establishing entanglement thresholds and protocols for resource-efficient quantum correlation recycling.

Contribution

It introduces a protocol based on probabilistic projective measurements to determine entanglement thresholds and sharing capacity in quantum networks.

Findings

Identified entanglement threshold for unbounded sharing

Derived trade-off between sharable branches and rounds

Extended protocol to realistic noise models

Abstract

Quantum networks are essential for advancing scalable quantum information processing. Quantum nonlocality sharing provides a crucial strategy for the resource-efficient recycling of quantum correlations, offering a promising pathway toward scaling quantum networks. Despite its potential, the limited availability of resources introduces a fundamental trade-off between the number of sharable network branches and the achievable sequential sharing rounds. The relationship between available entanglement and the sharing capacity remains largely unexplored, which constrains the efficient design and scalability of quantum networks. Here, we establish the entanglement threshold required to support unbounded sharing across an entire network by introducing a protocol based on probabilistic projective measurements. When resources fall below this threshold, we derive an achievable trade-off between the number of sharable branches and sharing rounds. To assess practical feasibility, we compare the detectability of our protocol with weak-measurement schemes and extend the sharing protocol to realistic noise models, providing a robust framework for nonlocality recycling in quantum networks.