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. 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 introduce and study a resource theory of this type of nonlocality which we term Buscemi nonlocality. We propose a geometric quantifier measuring the ability of a given state and local measurements to produce nonlocal correlations and establish its operational significance. In particular, we show that any distributed measurement which can demonstrate 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 nonlocality that can be generated using a given state is precisely equal to its entanglement content. Finally, we prove a quantitative relationship between: 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.
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. 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 introduce and study a resource theory of this type of nonlocality which we term Buscemi nonlocality. We propose a geometric quantifier measuring the ability of a given state and local measurements to produce nonlocal correlations and establish its operational significance. In particular, we show that any distributed measurement which can demonstrate 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 nonlocality that can be generated using a given state is precisely equal to its entanglement content. Finally, we prove a quantitative relationship between: 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.
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.
The standard benchmark for teleportation is the average fidelity of teleportation and according to this benchmark not all states are useful for teleportation.It was recently shown, however, that all entangled states lead to nonclassical teleportation, with there being no classical scheme able to reproduce the states teleported to Bob.Here we study the operational significance of this result.On the one hand, we demonstrate that every state is useful for teleportation if a generalization of the average fidelity of teleportation is considered which concerns teleporting quantum correlations.On the other hand, we show the strength of a particular entangled state and entangled measurement for teleportation-as quantified by the robustness of teleportation-precisely characterizes their ability to offer an advantage in the task of subchannel discrimination with side information.This connection allows us to prove that every entangled state outperforms all separable states when acting as a quantum memory in this discrimination task.Finally, within the context of a resource theory of teleportation, we show that the two operational tasks considered provide complete sets of monotones for two partial orders based on the notion of teleportation simulation, one classical and one quantum.
Nonlocality is one of the most important resources for quantum information protocols.The observation of nonlocal correlations in a Bell experiment is the result of appropriately chosen measurements and quantum states.We quantify the minimal purity to achieve a certain Bell value for any Bell operator.Since purity is the most fundamental resource of a quantum state, this enables us also to quantify the necessary coherence, discord, and entanglement for a given violation of two-qubit correlation inequalities.Our results shine a light on the Clauser-Horne-Shimony-Holt inequality by showing that for a fixed Bell violation an increase in the measurement resources does not always lead to a decrease of the minimal state resources.
A standard approach to quantifying resources is to determine which operations on the resources are freely available, and to deduce the partial order over resources that is induced by the relation of convertibility under the free operations. If the resource of interest is the nonclassicality of the correlations embodied in a quantum state, i.e., e n t a n g l e m e n t , then the common assumption is that the appropriate choice of free operations is Local Operations and Classical Communication (LOCC). We here advocate for the study of a different choice of free operations, namely, Local Operations and Shared Randomness (LOSR), and demonstrate its utility in understanding the interplay between the entanglement of states and the nonlocality of the correlations in Bell experiments. Specifically, we show that the LOSR paradigm (i) provides a resolution of the anomalies of nonlocality , wherein partially entangled states exhibit more nonlocality than maximally entangled states, (ii) entails new notions of genuine multipartite entanglement and nonlocality that are free of the pathological features of the conventional notions, and (iii) makes possible a resource-theoretic account of the self-testing of entangled states which generalizes and simplifies prior results. Along the way, we derive some fundamental results concerning the necessary and sufficient conditions for convertibility between pure entangled states under LOSR and highlight some of their consequences, such as the impossibility of catalysis for bipartite pure states. The resource-theoretic perspective also clarifies why it is neither surprising nor problematic that there are mixed entangled states which do not violate any Bell inequality. Our results motivate the study of LOSR-entanglement as a new branch of entanglement theory.
Quantum nonlocality, pioneered in Bell's seminal work and subsequently verified through a series of experiments, has drawn substantial attention due to its practical applications in various protocols. Evaluating and comparing the extent of nonlocality within distinct quantum correlations holds significant practical relevance. Within the resource theoretic framework this can be achieved by assessing the interconversion rate among different nonlocal correlations under free local operations and shared randomness. In this study we, however, present instances of quantum nonlocal correlations that are incomparable in the strongest sense. Specifically, when starting with an arbitrary many copies of one nonlocal correlation, it becomes impossible to obtain even a single copy of the other correlation, and this incomparability holds in both directions. Such incomparable quantum correlations can be obtained even in the simplest Bell scenario, which involves two parties, each having two dichotomic measurements setups. Notably, there exist an uncountable number of such incomparable correlations. Our result challenges the notion of a "unique gold coin," often referred to as the "maximally resourceful state," within the framework of the resource theory of quantum nonlocality. To this end, we provide examples of isotropic quantum correlations that cannot be distilled up to the Tsirelson point, and thus partially answer a long-standing open question in nonlocality distillation.
High-dimensional entanglement, captured by the Schmidt number, underpins advantages in quantum information tasks, yet a unified resource-theoretic description across different Buscemi-type operational objects has been missing. Here we develop a convex framework that treats bipartite states, distributed measurements, and teleportation instruments generated from shared entanglement on equal footing. For a fixed Schmidt-number threshold k, we introduce robustness-based monotones for each class of objects and prove a quantitative collapse: the Schmidt-number robustness of a bipartite state coincides with the maximal robustness achievable by any distributed measurement or teleportation instrument derived from that state. Consequently, within Buscemi-type operational frameworks, these objects do not carry independent high-dimensional resources but are governed by a single robustness-based monotone. We further provide a direct operational interpretation by relating this unique quantifier to the optimal advantage in entanglement-assisted state discrimination games. Our results complete a unified resource-theoretic characterization of high-dimensional entanglement across states, measurements, and quantum devices.