Sharing nonlocality in quantum network by unbounded sequential observers

TL;DR

This paper investigates how quantum nonlocality can be sequentially shared among multiple observers in quantum networks, revealing that unbounded sharing is possible in certain asymmetric and multi-input scenarios.

Contribution

It introduces the first analysis of sequential nonlocality sharing in quantum networks, extending to arbitrary inputs and parties, and identifies conditions for unbounded sharing.

Findings

In symmetric bilocality, at most two observers share nonlocality.

In asymmetric bilocality, up to six observers can share nonlocality.

In multi-party networks, unbounded sharing is possible with enough input settings.

Abstract

Of late, there has been an upsurge of interest in studying the sequential sharing of various forms of quantum correlations, viz., nonlocality, preparation contextuality, coherence, and entanglement. In this work, we explore the sequential sharing of nonlocality in a quantum network. We first consider the simplest case of the two-input bilocality scenario that features two independent sources and three parties, including two edge parties and a central party. We demonstrate that in the symmetric case when the sharing is considered for both the edge parties, the nonlocality can be shared by at most two sequential observers per edge party. However, in the asymmetric case, when the sharing across one edge party is considered, we show that at most, six sequential observers can share the nonlocality in the network. We extend our investigation to the two-input $n$-local scenario in the star-network configuration that features an arbitrary $n$ number of edge parties and one central party. In the asymmetric case, we demonstrate that the network nonlocality can be shared by an unbounded number of sequential observers across one edge party for a suitably large value of $n$. Further, we generalize our study for an arbitrary $m$ input $n$-local scenario in the star-network configuration. We show that even for an arbitrary $m$ input scenario, the nonlocality can be shared by an unbounded number of sequential observers. However, increasing the input $m$, one has to employ more number of edge parties $n$ than that of the two-input case to demonstrate the sharing of an unbounded number of sequential observers.