相关论文: Noncommutative probability in classical systems
A probabilistic propositional logic, endowed with an epistemic component for asserting (non-)compatibility of diagonizable and bounded observables, is presented and illustrated for reasoning about the random results of projective…
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 noncontextuality of quantum mechanics can be directly tested by measuring two entangled particles with more than two outcomes per particle. The two associated contexts are "interlinked" by common observables.
Experimentally, certain degrees of freedom may appear classical because their quantum fluctuations are smaller than the experimental error associated with measuring them. An approximation to a fully quantum theory is described in which the…
In the framework of certain general probability theories of single systems, we identify various nonclassical features such as incompatibility, multiple pure-state decomposability, measurement disturbance, no-cloning and the impossibility of…
Finding a physically consistent approach to modelling interactions between classical and quantum systems is a highly nontrivial task. While many proposals based on various mathematical formalisms have been made, most of these efforts run…
Non-classical probability (along with its underlying logic) is a defining feature of quantum mechanics. A formulation that incorporates them, inherently and directly, would promise a unified description of seemingly different prescriptions…
A review of various definitions of "compatibility" expressed in terms of ordinary probability, and a discussion of the occurrence of incompatibility (and the related phenomenon of interference) in non-quantal probabilistic systems.
Contextuality is a particular quantum phenomenon that has no analogue in classical probability theory. Given two independent systems, a natural question is how to represent such a situation as a single test space. In other words, how…
In classical stochastic theory, the joint probability distributions of a stochastic process obey by definition the Kolmogorov consistency conditions. Interpreting such a process as a sequence of physical measurements with probabilistic…
We present a formalism for studying the behaviour of quantum systems coupled to nonequilibrium environments exhibiting nonGaussian fluctuations. We discuss the role of a qubit as a detector of the statistics of environmental fluctuations,…
In his constructive and well-informed commentary, Andrei Khrennikov acknowledges a privileged status of classical probability theory with respect to statistical analysis. He also sees advantages offered by the Contextuality-by-Default…
We discuss the problem of separating consistently the total correlations in a bipartite quantum state into a quantum and a purely classical part. A measure of classical correlations is proposed and its properties are explored.
We explore the effect of two-dimensional position-space non-commutativity on the bipartite entanglement of continuous variable systems. We first extend the standard symplectic framework for studying entanglement of Gaussian states of…
The paper discusses the physical groundlessness of the models used for the derivation of canonical distribution and provides the experimental data demonstrating the incompleteness of quantum mechanics. The possibility of using statistical…
We investigate quantum effects in the evolution of general systems. For studying such temporal quantum phenomena, it is paramount to have a rigorous concept and profound understanding of the classical dynamics in such a system in the first…
Hybrid classical-quantum models are computational schemes that investigate the time evolution of systems, where some degrees of freedom are treated classically, while others are described quantum-mechanically. First, we present the…
The task of testing whether quantum theory applies to all physical systems and all scales requires considering situations where a quantum probe interacts with another system that need not obey quantum theory in full. Important examples…
A homogeneous and isotropic cosmological model with a positive cosmological constant is considered. The matter sector is given by a massless scalar field, which can be used as an internal time to deparametrize the theory. The idea is to…
This paper has two purposes. One is to demonstrate contextuality analysis of systems of epistemic random variables. The other is to evaluate the performance of a new, hierarchical version of the measure of (non)contextuality introduced in…