Related papers: Another quantum version of Sanov theorem
We study the impact of quantum computation on the fundamental problem of testing the property of distributions. In particular, we focus on testing whether two unknown classical distributions are close or far enough, and propose the…
Although classical mechanics and quantum mechanics are separate disciplines, we live in a world where Planck's constant \hbar>0, meaning that the classical and quantum world views must actually {\it coexist}. Traditionally, canonical…
Possible generalizations of quantum theory permitting to describe in a unique way the development of the quantum system and the measurement process are discussed. The approach to the problem based on the Lindblad's equation for the…
We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical…
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…
In order to relate the probabilistic predictions of quantum theory uniquely to measurement results, one has to conceive of an ensemble of identically prepared copies of the quantum system under study. Since the universe is the total domain…
The paper attempts to convince that the orthodox interpretation of quantum mechanics does not contradict philosophical realism by throwing light onto certain properties of quantum systems that seem to have escaped attention as yet. The…
In classical statistical decision theory, comparison of experiments plays very important role. Especially, so-called randomization criteria is most important. In this paper, we establish two kinds of quantum analogue these concepts, and…
Randomness is an intrinsic feature of quantum theory. The outcome of any quantum measurement will be random, sampled from a probability distribution that is defined by the measured quantum state. The task of sampling from a prescribed…
By formulating the axioms of quantum mechanics, von Neumann also laid the foundations of a "quantum probability theory". As such, it is regarded a generalization of the "classical probability theory" due to Kolmogorov. Outside of quantum…
A unifying principle explaining the numerical bounds of quantum correlations remains elusive despite the efforts devoted to identifying it. Here we show that these bounds are indeed not exclusive to quantum theory: for any abstract…
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…
The stochastic theory of relativistic quantum mechanics presented here is modelled on the one that has been proposed previously and that was claimed to be a promising substitute to the orthodox theory in the non-relativistic domain. So it…
In any given experimental scenario, the rules of quantum theory provide statistical distributions that the observed outcomes are expected to follow. The set formed by all these distributions contains the imprint of quantum theory, capturing…
The different interpretations of quantum mechanics yield the same experimental results, which may give the impression that the question of what interpretation is the true one, is a philosophical question, not a scientific one. But in this…
In the limit of large quantum excitations, the classical and quantum probability distributions for a Schr\"odinger equation can be compared by using the corresponding WKBJ solutions whose rapid oscillations are averaged. This result is…
Two complementary observables can be measured simultaneously so that the exact individual distributions can be recovered by a proper data inversion. We apply this program to the paradigmatic example of the Young interferometer from the…
The purpose of the paper is to study the condition for a probability distribution family to a quantum state family. This is an (relatively) easy example of quantum version of "comparison of statistical experiments", which had turned out to…
As a generalization of the Fourier transform, the fractional Fourier transform was introduced and has been further investigated both in theory and in applications of signal processing. We obtain a sampling theorem on shift-invariant spaces…
Recently Dzhafarov and Kon published the paper advertising the possibility to use the coupling technique of classical probability theory to model incompatible observables in quantum physics and quantum-like models of psychology. Here I…