We present a device-independent protocol to test if a given black-box measurement device is entangled, that is, has entangled eigenstates. Our scheme involves three parties and is inspired by entanglement swapping; the test uses the Clauser-Horne-Shimony-Holt Bell inequality, checked between each pair of parties. In the case where all particles are qubits, we characterize quantitatively the deviation of the measurement device from a perfect Bell-state measurement.
In this Letter we compute an analogue of Tsirelson's bound for Hardy's test of nonlocality, that is, the maximum violation of locality constraints allowed by the quantum formalism, irrespective of the dimension of the system. The value is found to be the same as the one achievable already with two-qubit systems, and we show that only a very specific class of states can lead to such maximal value, thus highlighting Hardy's test as a device-independent self-test protocol for such states. By considering realistic constraints in Hardy's test, we also compute device-independent upper bounds on this violation and show that these bounds are saturated by two-qubit systems, thus showing that there is no advantage in using higher-dimensional systems in experimental implementations of such test.Introduction.-The development of quantum information science is based on a recurrent pattern: nonclassical features of quantum physics, previously considered as mind-boggling and worth only of philosophical chat, are found to have an operational meaning and even to be potentially useful for applications. One of the discoveries that triggered this development is the prediction and observation of the violation of Bell inequalities [1]. This observation implies that correlations obtained by measuring separated quantum systems locally cannot be simulated classically without communication, a fact that is often referred to as nonlocality.Within quantum information, nonlocality has undergone an interesting parable. For many years, it has been put aside as having fulfilled its role: the loathed local variables models having been disposed of forever, one could peacefully concentrate on entanglement theory. Only few researchers kept on believing that this very intriguing observation could be useful for something in itself. The latter view was vindicated a few years ago, when it was noticed that nonlocality allows device-independent assessments: indeed, nonlocality is assessed only from the input-output statistics of the measurement, without reference to the degree of freedom that is being measured. This powerful type of assessment is sensitive to the existence of undesired sidechannels and will be ideal for certification of future quantum devices. So far, device-independent results are available for the security of quantum cryptography [2,3], the quality of sources [4,5] and measurement devices [6], the amount of randomness that one can generate [7,8]. In this paper, we study the possibility of device-independent assessment of one of the earliest proposals to check nonlocality: it used to be called Hardy's paradox but, in the spirit of quantum informa-
Entanglement allows for the nonlocality of quantum theory, which is the resource behind device-independent quantum information protocols. However, not all entangled quantum states display nonlocality, and a central question is to determine the precise relation between entanglement and nonlocality. Here we present the first general test to decide whether a quantum state is local, and that can be implemented by semidefinite programming. This method can be applied to any given state and for the construction of new examples of states with local hidden-variable models for both projective and general measurements. As applications we provide a lower bound estimate of the fraction of two-qubit local entangled states and present new explicit examples of such states, including those which arise from physical noise models, Bell-diagonal states, and noisy GHZ and W states.Introduction.-Entanglement is one of the defining properties of quantum theory, playing a central role in quantum information science. One of the most astonishing consequences of entanglement is that local measurements on composite quantum systems can produce correlations which are impossible to reproduce by any classical mechanism satisfying natural notions of local causality [1]. Such correlations are the key aspect behind the famous nonlocality of quantum theory, and they are witnessed by the violation of Bell inequalities [2]. Witnessing nonlocality certifies the entanglement of the underlying quantum state in a way which makes no assumptions about the functioning of the apparatuses used, a realisation which led to the development of the field of deviceindependent quantum information.
We present a method that allows the study of classical and quantum correlations in networks with causally independent parties, such as the scenario underlying entanglement swapping. By imposing relaxations of factorization constraints in a form compatible with semidefinite programming, it enables the use of the Navascués-Pironio-Acín hierarchy in complex quantum networks. We first show how the technique successfully identifies correlations not attainable in the entanglement-swapping scenario. Then we use it to show how the nonlocal power of measurements can be activated in a network: there exist measuring devices that, despite being unable to generate nonlocal correlations in the standard Bell scenario, provide a classical-quantum separation in an entanglement swapping configuration.Quantum correlations are at the core of quantum information science [1,2]. As proven by the violation of Bell inequalities [3], quantum theory is nonlocal, in the sense that there exist correlations between outcomes of measurements performed on distant entangled quantum systems that are incompatible with any explanation involving just local hidden variables (LHV). Quantum nonlocality is a powerful resource that grounds protocols for secure cryptography [4][5][6], randomness certification [7,8], self-testing [9] or distributed computing [10]. Therefore, it is crucial to develop ways to test the incompatibility of a given correlation with LHV models, that is, to detect whether the correlation contains some nonlocal features that can be harnessed.Nowadays, fast progress towards advanced demonstrations of quantum communication networks require to go beyond the two-party scenario and characterize networks of growing complexity, providing the tools to witness the nonclassicality of quantum correlations. To that aim, the framework of causal networks [11] and its quantum generalizations [12][13][14][15][16][17][18] have played an insightful role. Causal networks not only allow to derive Bell's theorem from a causal inference perspective [19,20] but also provide generalizations to more complex scenarios such as quantum networks with several sources [12,[21][22][23] or involving communication among the parties [24][25][26].Despite all recent advances, the understanding of the structure of correlations in networks remains very limited. The most general method to characterize classical network correlations relies on algebraic geometry [27] that, in practice, is limited to very simple cases. Moti-vated by that, alternative methods have been proposed that either are limited to very specific networks [22,23], or do not have a clear path for a quantum generalization [21,[28][29][30]. An important recent advance is the development of the inflation technique [29,31], that allows for the characterization of classical and general, nonsignaling network correlations. Obtaining an analogous method to discriminate between quantum and supraquantum correlations is a subject of current research [32], but to date, the only known method for quantum correlations, ...
We consider Bell tests involving bipartite states shared between three parties. We show that the simple inclusion of a third part may greatly simplify the measurement scenario (in terms of the number of measurement settings per part) and allows the identification of previously unknown nonlocal resources.
Abstract. Non-contextuality (NC) and Bell inequalities can be expressed as bounds Ω for positive linear combinations S of probabilities of events, S ≤ Ω. Exclusive events in S can be represented as adjacent vertices of a graph called the exclusivity graph of S. In the case that events correspond to the outcomes of quantum projective measurements, quantum probabilities are intimately related to the Grötschel-Lovász-Schrijver theta body of the exclusivity graph. Then, one can easily compute an upper bound to the maximum quantum violation of any NC or Bell inequality by optimizing S over the theta body and calculating the Lovász number of the corresponding exclusivity graph. In some cases, this upper bound is tight and gives the exact maximum quantum violation. However, in general, this is not the case. The reason is that the exclusivity graph does not distinguish among the different ways exclusivity can occur in Bell-inequality (and similar) scenarios. An interesting question is whether there is a graph-theoretical concept which accounts for this problem. Here we show that, for any given N -partite Bell inequality, an edge-coloured multigraph composed of N single-colour graphs can be used to encode the relationships of exclusivity between each party's parts of the events. Then, the maximum quantum violation of the Bell inequality is exactly given by a refinement of the Lovász number that applies to these edge-coloured multigraphs. We show how to calculate upper bounds for this number using a hierarchy of semi-definite programs and calculate upper bounds for I 3 , I 3322 and the three bipartite Bell inequalities whose exclusivity graph is a pentagon. The multigraph-theoretical approach introduced here may remove some obstacles in the program of explaining quantum correlations from first principles.
Incompatibility of observables, or measurements, is one of the key features of quantum mechanics, related, among other concepts, to Heisenberg's uncertainty relations and Bell nonlocality. In this manuscript we show, however, that even though incompatible measurements are necessary for the violation of any Bell inequality, some relevant Bell-like inequalities may be obtained if compatibility relations are assumed between the local measurements of one (or more) of the parties. Hence, compatibility of measurements is not necessarily a drawback and may, however, be useful for the detection of Bell nonlocality and device-independent certification of entanglement.
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