Related papers: Bell's Inequalities and Algebraic Structure
It is known that the local bound of a Bell inequality is sensitive to the knowledge of the external observer about the settings statistics. Here we ask how that sensitivity depends on the structure of that knowledge. It turns out that in…
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 a consequence of measurement incompatibility (not, as generally thought, of nonlocality). In classical terms, this is equivalent to contextuality -- measurement devices do have a significant effect. Contextual models…
The Bell's inequalities are derived from the hypotheses of Locality, Realism and (what is lesser known) the equality between the factual and the counterfactual time averages of the expectation values of observables. The necessity of a…
It is shown that Bell's counterfactuals admit joint quasiprobability distributions (i.e. joint distributions exist, but may not be non-negative). A necessary and sufficient condition for the existence among them of a true probability…
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…
It is argued that the lesson we should learn from Bell's inequalities is not that quantum mechanics requires some kind of action at a distance, but that it leads us to believe in parallel worlds.
We present a generalization of the notion of an algebra norm relevant to real finite-dimensional unital associative algebras. Among other things, this leads to a novel set of algebra isomorphism invariants, some of which are computationally…
The derivation of Bell inequalities in terms of quantum statistical (thermodynamic) entropies is considered. Inequalities of the Wigner form are derived but shown to be extremely limiting in their applicability due to the nature of the…
We introduce Bell inequalities based on covariance, one of the most common measures of correlation. Explicit examples are discussed, and violations in quantum theory are demonstrated. A crucial feature of these covariance Bell inequalities…
Since John S. Bell demonstrated the interest of studying linear combinations of probabilities in relation with the EPR paradox in 1964, Bell inequalities have lead to numerous developments. Unfortunately, the description of Bell…
The problem of characterizing classical and quantum correlations in networks is considered. Contrary to the usual Bell scenario, where distant observers share a physical system emitted by one common source, a network features several…
We show that the symmetrization of a brace algebra structure yields the structure of a symmetric brace algebra.
We establish an inequality of different metrics for algebraic polynomials.
Which nonlocal correlations can be obtained, when a party has access to more than one subsystem? While traditionally nonlocality deals with spacelike separated parties, this question becomes important with quantum technologies that connect…
We will demonstrate in this paper that Bell's theorem (Bell's inequality) does not really conflict with quantum mechanics, the controversy between them originates from the different definitions for the expectation value using the…
The Bell inequalities in three and four correlations are re-derived in general forms showing that three and four data sets, respectively, identically satisfy them regardless of whether they are random, deterministic, measured, predicted, or…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
Proofs of Bell's theorem and the data analysis used to show its violation have commonly assumed a spatially stationary underlying process. However, it has been shown recently that the appropriate Bell's inequality holds identically for…
We study the relation between the quantum games, communication complexity problems and Bell inequalities. In particular we are interested in answering the question whether for every element of one of these groups there is a corresponding…