Related papers: Statistics on Lefschetz thimbles: Bell/Leggett-Gar…
The Leggett-Garg inequalities are a set of inequalities obeyed by classical systems but violated in quantum theory. Their violation has been taken as evidence that quantum theory lacks a `realistic' formulation. However in addition to…
Contextuality means non-existence of a joint distribution for random variables recorded under mutually incompatible conditions, subject to certain constraints imposed on how the identity of these variables may change across these…
Bell inequalities play a central role in the study of quantum non-locality and entanglement, with many applications in quantum information. Despite the huge literature on Bell inequalities, it is not easy to find a clear conceptual answer…
We derive a set of Leggett-Garg inequalities (temporal Bell's inequalities) for the moment generating function of charge transferred through a conductor. Violation of these inequalities demonstrates the absence of a macroscopic-real…
We propose a new Wigner inequality suitable for test of the hypothesis of realism. We show that this inequality is not identical neither to the well-known Wigner inequality nor to the Leggett-Garg inequality in Wigner form. The obtained…
The assumptions required for the derivation of Bell inequalities are not usually satisfied for random fields in which there are any thermal or quantum fluctuations, in contrast to the general satisfaction of the assumptions for classical…
We show that the noncontextual inequality proposed by Klyachko et al. [Phys. Rev. Lett. 101, 020403 (2008)] belongs to a broader family of inequalities, one associated to each compatibility structure of a set of events (a graph), and its…
We show that (in contrast to a rather common opinion) QM is not a complete theory. This is a statistical approximation of classical statistical mechanics on the {\it infinite dimensional phase space.} Such an approximation is based on the…
The basic Leggett inequalities, i.e. those inequalities in which the particular assumptions of Leggett's hidden-variable model (e.g. Malus law) were not yet introduced, are usually derived using hidden-variable distributions of…
It remains an open question how realist view of macroscopic world emerges from quantum formalism. For testing the macrorealism in quantum domain, an interesting approach was put forward by Leggett and Garg in $1985$, by formulating a…
In 1862, George Boole derived an inequality for variables, now known as Boolean variables, that in his opinion represents a demarcation line between possible and impossible experience. This inequality forms an important milestone in the…
Quantum mechanics presents peculiar properties that, on the one hand, have been the subject of several theoretical and experimental studies about its very foundations and, on the other hand, provide tools for developing new technologies,…
The Leggett-Garg inequalities probe the classical-quantum boundary by putting limits on the sum of pairwise correlation functions between classical measurement devices that consecutively measured the same quantum system. The apparent…
We derive a Bell-like inequality involving all correlations in local observables with uncertainty free states and show that the inequality is violated in quantum mechanics for EPR and GHZ states. If the uncertainties are allowed in local…
It is shown that the Bell inequalities are closely related to the triangle inequalities involving distance functions amongst pairs of random variables with values $\left\{ 0,1\right\} $. A hidden variables model may be defined as a mapping…
In this paper, we discuss questions related to the renormalizability of the classical statistical approximation, an approximation scheme that has been used recently in several studies of out-of-equilibrium problems in Quantum Field Theory.…
The quantum description of the microscopic world is incompatible with the classical description of the macroscopic world, both mathematically and conceptually. Nevertheless, it is generally accepted that classical mechanics emerges from…
In this paper we propose a time-independent \textit{equality} and time-dependent \textit{inequality}, suitable for an experimental test of the hypothesis of realism. The derivation of these relations is based on the concept of conditional…
We consider information-theoretic inequalities of the Bell type in the presence of decoherence. It is natural that too strong coupling with the environment can prevent an observation of quantum correlations. In this regard, the use 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…