Related papers: The extension problem for partial Boolean structur…
We present critical arguments against individual interpretation of Bohr's complementarity and Heisenberg's uncertainty principles. Statistical interpretation of these principles is discussed in the contextual framework. We support the…
Discrepancy between periodic orbit theory and numerical calculation of a modified Kepler problem is cleared by a quantum mechanical calculation. The diagonal approximation already gives a good fit for the numerical calculation. A better…
Severe methodological and numerical problems of the traditional quantum mechanical approach to the description of molecular systems are outlined. To overcome these, a simple alternative to the Born-Oppenheimer approximation is presented on…
Bell inequalities follow from a set of seemingly natural assumptions about how to provide a causal model of a Bell experiment. In the face of their violation, two types of causal models that modify some of these assumptions have been…
This paper analyzes three forms of representation of Boolean functions, such as Classical, Algebraic and Reed-Muller. The concept of intersection and subsets of representation forms have been introduced, moreover suitable criteria for…
Three extensions and reinterpretations of nonclassical probabilities are reviewed. (i) We propose to generalize the probability axiom of quantum mechanics to self-adjoint positive operators of trace one. Furthermore, we discuss the…
Several arguments demonstrate the incompatibility between Quantum Mechanics and classical Physics. Bell's inequalities and Greenberger-Horne-Zeilinger (GHZ) arguments apply to specific non-classical states. The Kochen-Specker (KS) one,…
Partial Boolean algebra underlies the quantum logic as an important tool for quantum contextuality. We propose the notion atom graphs to reveal the graph structure of partial Boolean algebra for finite dimensional quantum systems by proving…
We consider classical and entanglement-assisted versions of a distributed computation scheme that computes nonlinear Boolean functions of a set of input bits supplied by separated parties. Communication between the parties is restricted to…
A non-Boolean extension of the classical probability model is proposed. The non-Boolean probabilities reproduce typical quantum phenomena. The proposed model is more general and more abstract, but easier to interpret, than the quantum…
The interpretation of quantum mechanics has been a problem since its founding days. A large contribution to the discussion of possible interpretations of quantum mechanics is given by the so-called impossibility proofs for hidden variable…
The fundamental algebraic concepts of quantum mechanics, as expressed by many authors, are reviewed and translated into the framework of the relatively new non-distributive system of Boolean fractions (also called conditional events or…
Nonlocality and contextuality are at the root of conceptual puzzles in quantum mechanics, and are key resources for quantum advantage in information-processing tasks. Bell nonlocality is best understood as the incompatibility between…
The failure of distributivity in quantum logic is motivated by the principle of quantum superposition. However, this principle can be encoded differently, i.e., in different logico-algebraic objects. As a result, the logic of experimental…
In this paper, a modified formulation of generalized probabilistic theories that will always give rise to the structure of Hilbert space of quantum mechanics, in any finite outcome space, is presented and the guidelines to how to extend…
The aim of the paper is to derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The main extensions, which also can be motivated from an applied statistics point…
The predictions of quantum mechanics cannot be resolved with a completely classical view of the world. In particular, the statistics of space-like separated measurements on entangled quantum systems violate a Bell inequality. We put forward…
The tomographic approach to quantum mechanics is revisited as a direct tool to investigate violation of Bell-like inequalities. Since quantum tomograms are well defined probability distributions, the tomographic approach is emphasized to be…
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…
There are two powerful arguments against the possibility of extending quantum mechanics, the violation of Bell inequalities and the Kochen-Specker theorem, but the connection between the two remains confused. Following the distinctive…