Operational Significance Of The Quantum Resource Theory Of Buscemi Nonlocality

Although entanglement is necessary for observing nonlocality in a Bell experiment, there are entangled states that can never be used to demonstrate nonlocal correlations. In a seminal paper Buscemi [Phys. Rev. Lett. 108, 200401 (2012)] 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 prove the following results. First, we show that any distributed measurement that can demonstrate Buscemi nonlocal correlations provides strictly better performance than any distributed measurement that does not use entanglement in the task of distributed state discrimination, and that this advantage is quantified by the geometric quantifier we propose, thus establishing its operational significance. Second, we prove a quantitative relationship between Buscemi nonlocality, the ability to perform nonclassical teleportation, and entanglement. In particular, we show that the maximal amount of Buscemi nonlocality that can be generated using a given state is precisely equal to its entanglement content. Using this relationship, we propose new discrimination tasks for which nonclassical teleportation and entanglement lead to an advantage over their classical counterparts. Third, we interpret Buscemi nonlocality from the perspective of information theory and show that it is related to a single-shot capacity of a quantum-to-classical bipartite channel.