Related papers: Principle of supplementarity: contextual probabili…
Contextuality is usually defined as absence of a joint distribution for a set of measurements (random variables) with known joint distributions of some of its subsets. However, if these subsets of measurements are not disjoint,…
Contextuality provides a unifying paradigm for nonclassical aspects of quantum probabilities and resources of quantum information. Unfortunately, most forms of quantum contextuality remain experimentally unexplored due to the difficulty of…
In quantum mechanics, the selfadjoint Hilbert space operators play a triple role as observables, generators of the dynamical groups and statistical operators defining the mixed states. One might expect that this is typical of Hilbert space…
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…
By the example of a Fourier transform, the possibilities of Hilbert space geometry applications for statistical model construction are analyzed. In accordance with Bohr's complementarity principle, mutually-complementary coordinate and…
From behavioral sciences to biology to quantum mechanics, one encounters situations where (i) a system outputs several random variables in response to several inputs, (ii) for each of these responses only some of the inputs may "directly"…
The concept of emergence is critically analyzed in particular with respect to the assumed emergence of mental properties from a neuronal basis. We argue that so-called contextual emergence is needed to avoid an eliminatory reductionism.…
Starting with a consideration of the implication of Bell inequalities in quantum mechanics, a new quantum postulate is suggested in order to restore classical locality and causality to quantum physics: only the relative coordinates between…
Bohr's interpretation of quantum mechanics has been criticized as incoherent and opportunistic, and based on doubtful philosophical premises. If so Bohr's influence, in the pre-war period of 1927-1939, is the harder to explain, and the…
In the quantum mechanical Hilbert space formalism, the probabilistic interpretation is a later ad-hoc add-on, more or less enforced by the experimental evidence, but not motivated by the mathematical model itself. A model involving a clear…
Models of a phenomenon are often developed by examining it under different experimental conditions, or measurement contexts. The resultant probabilistic models assume that the underlying random variables, which define a measurable set of…
The history of complementary observables and mutual unbiased bases is reviewed. A characterization is given in terms of conditional entropy of subalgebras. The concept of complementarity is extended to non-commutative subalgebras.…
This paper presents a framework for Quantum causal modeling based on the interpretation of causality as a relation between an observer's probability assignments to hypothetical or counterfactual experiments. The framework is based on the…
The contextuality and noncontextuality notions are considered in framework of probability representation of quantum states. Example of qutrit states and violation of the noncontextuality inequalities are presented by using the spin tomogram…
The non-classicality of single quantum systems can be formalised using the notion of contextuality. But can contextuality be convincingly demonstrated in an experiment, without reference to the quantum formalism? The operational approach to…
Physics relies on mathematical spaces carefully matched to the phenomena under study. Phase space in classical mechanics, Hilbert space in quantum theory, configuration spaces in field theory all provide representations in which physical…
Recently, a measure has been put forward which allows for the quantification of the degree of reality of an observable for a given preparation [A. L. O. Bilobran and R. M. Angelo, Europhys. Lett. 112, 40005 (2015)]. Here we employ this…
In quantum theory, a measurement context is defined by an orthogonal basis in a Hilbert space, where each basis vector represents a specific measurement outcome. The precise quantitative relation between two different measurement contexts…
One of the key features of quantum mechanics is the interference of probability amplitudes. The reason for the appearance of interference is mathematically very simple. It is the linear structure of the Hilbert space which is used for the…
Analysing Quantum Measurement requires analysing the physics of amplification since amplification of phenomena from one scale to another scale is essential to measurement. There still remains the task of working this into an axiomatic…