The operational significance of the quantum resource theory of Buscemi nonlocality

TL;DR

This paper explores the resource theory of Buscemi nonlocality, demonstrating its operational significance, its relation to entanglement, and its advantages in quantum state discrimination and teleportation tasks.

Contribution

It introduces a geometric measure of Buscemi nonlocality, establishes its equivalence to entanglement, and links it to nonclassical teleportation, advancing understanding of quantum nonlocal resources.

Findings

Buscemi nonlocality can be quantified geometrically.

Demonstrates that Buscemi nonlocality outperforms classical measurements in state discrimination.

Shows that maximal Buscemi nonlocality equals a state's entanglement content.

Abstract

Although entanglement is necessary for observing nonlocality in a Bell experiment, there are entangled states which can never be used to demonstrate nonlocal correlations. In a seminal paper [PRL 108, 200401 (2012)] F. Buscemi extended the standard Bell experiment by allowing Alice and Bob to be asked quantum, instead of classical, questions. This gives rise to a broader notion of nonlocality, one which can be observed for every entangled state. In this work we study a resource theory of this type of nonlocality referred to as Buscemi nonlocality. We propose a geometric quantifier measuring the ability of a given state and local measurements to produce Buscemi nonlocal correlations and establish its operational significance. In particular, we show that any distributed measurement which can demonstrate Buscemi nonlocal correlations provides strictly better performance than any distributed measurement which does not use entanglement in the task of distributed state discrimination. We also show that the maximal amount of Buscemi nonlocality that can be generated using a given state is precisely equal to its entanglement content. Finally, we prove a quantitative relationship between: Buscemi nonlocality, the ability to perform nonclassical teleportation, and entanglement. Using this relationship we propose new discrimination tasks for which nonclassical teleportation and entanglement lead to an advantage over their classical counterparts.