Related papers: George Boole and the Bell inequalities
Entanglement is a critical resource used in many current quantum information schemes. As such entanglement has been extensively studied in two qubit systems and its entanglement nature has been exhibited by violations of the Bell…
Bell inequalities are central tools for studying nonlocal correlations and their applications in quantum information processing. Identifying inequalities for many particles or measurements is, however, difficult due to the computational…
The logical foundations of Bell's inequality are reexamined. We argue that the form of the reality condition that underpins Bell's inequality comes from the requirement of solving the quantum measurement problem. Hence any violation of…
Bell inequalities, understood as constraints between classical conditional probabilities, can be derived from a set of assumptions representing a common causal explanation of classical correlations. A similar derivation, however, is not…
Bell derived the given inequalities on the basis of one rather forceful assumption that was supposed to hold in the hidden variable theory. However, this assumption has been so strong that it has corresponded only to the classical physics;…
In this paper we consider the possible correlations between two parties using local machines and shared randomness with an additional amount of classical communication. This is a continuation of the work initiated by Bacon and Toner in Ref.…
An abstract treatment of Bell inequalities is proposed, in which the parameters characterizing Bell's observable can be times rather than directions. The violation of a Bell inequality might then be taken to mean that a property of a system…
Bell inequalities are mathematical constructs that demarcate the boundary between quantum and classical physics. A new class of multiplicative Bell inequalities originating from a volume maximization game (based on products of correlators…
By taking into account that all real measurements are performed successively, during time, it is concluded that the violation of the Bell's inequalities in the Nature does not refute (even in an ideally perfect experiment) the theories…
In a previous publication, we showed how group actions can be used to generate Bell inequalities. The group action yields a set of measurement probabilities whose sum is the basic element in the inequality. The sum has an upper bound if the…
With Bell's inequalities one has a formal expression to show how essentially all local theories of natural phenomena that are formulated within the framework of realism may be tested using a simple experimental arrangement. For the case of…
The relation between the boolean functions and Bell inequalities for qubits is analyzed. The connection between the maximal quantum violation of a Bell inequality and the nonlinearity of the corresponding boolean function is discussed. A…
Experimental tests of Bell inequalities ought to take into account all detection events. If the latter are postselected, and only some of these events are included in the statistical analysis, a Bell inequality may be violated, even by…
Bell's inequality sets a strict threshold for how strongly correlated the outcomes of measurements on two or more particles can be, if the outcomes of each measurement are independent of actions undertaken at arbitrarily distant locations.…
Over the past few decades, experimental tests of Bell-type inequalities have been at the forefront of understanding quantum mechanics and its implications. These strong bounds on specific measurements on a physical system originate from…
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…
We give an overview and conceptual discussion of some of our results on contextuality and non-locality. We focus in particular on connections with the work of Itamar Pitowsky on correlation polytopes, Bell inequalities, and Boole's…
From the beginning of quantum mechanics, there has been a discussion about the concept of reality, as exemplified by the EPR paradox. To many, the idea of the paradox and the possibility of local hidden variables was dismissed by the Bell…
We discuss a class of proofs of Bell-type inequalities that are based on tables of potential outcomes. These proofs state in essence: if one can only imagine (or write down in a table) the potential outcome of a hidden parameter model for…
The well known inequalities of John S. Bell may be regarded, from a purely mathematical viewpoint, as a direct consequence of Vorob'ev-type topological-combinatorial cyclicities formed with functions on a common probability space. However,…