Related papers: Quaternions, octonions and Bell-type inequalities
Derivation of the full set of Bell inequalities involving correlation functions, for two parties, with binary observables, and N possible local settings is not as easy as it seemed. The proof of v1 is wrong. Additionaly one can find a…
In this note, by the umbra calculus method, the Sun and Zagier's congruences involving the Bell numbers and the derangement numbers are generalized to the polynomial cases. Some special congruences are also provided.
Bell-inequality checks constitute a probe of entanglement -- given a source of entangled particles, their violation are a signature of the non-local nature of quantum mechanics. Here, we study a solid state device producing pairs of…
We extend the Bell inequality known for two qubits to the four-level atom, including an artificial atom realized by the superconducting circuit, and qudit with j=3/2. We formulate the extended inequality as the inequality valid for an…
It is a recent realization that many of the concepts and tools of causal discovery in machine learning are highly relevant to problems in quantum information, in particular quantum nonlocality. The crucial ingredient in the connection…
Tight Bell inequalities are facets of Pitowsky's correlation polytope and are usually obtained from its extreme points by solving the hull problem. Here we present an alternative method based on a combination of algebraic results on…
Bell inequalities are relevant for many problems in quantum information science, but finding them for many particles is computationally hard. Recently, a computationally feasible method called cone-projection technique has been developed to…
Bell inequalities constitute a key tool in quantum information theory: they not only allow one to reveal nonlocality in composite quantum systems, but, more importantly, they can be used to certify relevant properties thereof. We provide a…
In a quantum network, distant observers sharing physical resources emitted by independent sources can establish strong correlations, which defy any classical explanation in terms of local variables. We discuss the characterization of…
Bell's inequality plays an important role with respect to the Einsteinian question about the physical reality of quantum theory. While Bell's inequality is usually viewed within the geometric framework of a Hilbert space quantum model, the…
Which is the simplest logical structure for which there is quantum nonlocality? We show that there are only three bipartite Bell inequalities with quantum violation associated with the simplest graph of relationships of exclusivity with a…
Contemporary understanding of correlations in quantum many-body systems and in quantum phase transitions is based to a large extent on the recent intensive studies of entanglement in many-body systems. In contrast, much less is known about…
We develop a novel approach to Bell inequalities based on a constraint that the correlations exhibited by local realistic theories must satisfy. This is used to construct a family of Bell inequalities for bipartite quantum systems of…
Local systems may appear to violate Bell's inequalities if they are observed through suitable filters. The nonlocality leading to violation is outside the system and comprises the observer comparing the outcomes of the typical two wing Bell…
We present a set of Bell inequalities which are sufficient and necessary for separability of general pure multipartite quantum states in arbitrary dimensions. The relations between Bell inequalities and distillability are also studied. We…
We present a family of Bell inequalities involving only two measurement settings of each party for N>2 qubits. Our inequalities include all the standard ones with fewer than N qubits and thus gives a natural generalization. It is shown that…
The no-signaling polytope associated to a Bell scenario with three parties, two inputs, and two outputs is found to have 53856 extremal points, belonging to 46 inequivalent classes. We provide a classification of these points according to…
Non-classical quantum correlations underpin both the foundations of quantum mechanics and modern quantum technologies. Among them, Bell nonlocality is a central example. For bipartite Bell inequalities, nonlocal correlations obey strict…
Bell nonlocality -- the existence of quantum correlations that cannot be explained by classical means -- is certainly one of the most striking features of quantum mechanics. Its range of applications in device-independent protocols is…
We study a class of Bell inequalities and find their maximum quantum violation. These inequalities involve n parties, two measurements per party, with each measurement having two outcomes. The n=2 case corresponds to the CH inequality. We…