Related papers: A Factor-Graph Representation of Probabilities in …
We present a trivial probabilistic illustration for representation of quantum mechanics as an algorithm for approximative calculation of averages.
The tomographic invertable map of the Wigner function onto the positive probability distribution function is studied. Alternatives to the Schr\"odinger evolution equation and to the energy level equation written for the positive probability…
This paper extends quantile factor analysis to a probabilistic variant that incorporates regularization and computationally efficient variational approximations. We establish through synthetic and real data experiments that the proposed…
A general analytical approach to the statistical description of quantum graph spectra based on the exact periodic orbit expansions of quantum levels is discussed. The exact and approximate expressions obtained in \cite{Anima} for the…
Multiparametric statistical model providing stable reconstruction of parameters by observations is considered. The only general method of this kind is the root model based on the representation of the probability density as a squared…
Graph states are the backbone of measurement-based continuous-variable quantum computation. However, experimental realisations of these states induce Gaussian measurement statistics for the field quadratures, which poses a barrier to obtain…
Based on a recent development in the area of error control coding, we introduce the notion of convolutional factor graphs (CFGs) as a new class of probabilistic graphical models. In this context, the conventional factor graphs are referred…
It is shown that the statistical conception of quantum mechanics is dynamical but not probabilistic, i.e. the statistical description in quantum mechanics is founded on dynamics. A use of the probability theory, when it takes place, is…
Several finite dimensional quasi-probability representations of quantum states have been proposed to study various problems in quantum information theory and quantum foundations. These representations are often defined only on restricted…
This brief article gives an overview of quantum mechanics as a {\em quantum probability theory}. It begins with a review of the basic operator-algebraic elements that connect probability theory with quantum probability theory. Then quantum…
An analysis is made of a moving disturbance using a directed cyclic graph. A statistical approach is used to calculate the alternative positions in space and state of the disturbance with a defined observed time. The probability for a…
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…
Tomographic probability representation is introduced for fermion fields. The states of the fermions are mapped onto probability distribution of discrete random variables (spin projections). The operators acting on the fermion states are…
Quantum probabilities are defined for several important physical cases characterizing measurements with multimode quantum systems. These are the probabilities for operationally testable measurements, for operationally uncertain…
Partial symplectic conditional and joint probability representations of quantum mechanics are considered. The correspondence rules for most interesting physical operators are found and the expressions of the dual symbols of operators are…
Statistical functions such as the moment-generating function, characteristic function, cumulant-generating function, and second characteristic function are cornerstone tools in classical statistics and probability theory. They provide a…
A number of phenomena generally believed characteristic of quantum mechanics and seen as interpretively problematic--the incompatibility and value-indeterminacy of variables, the non-existence of dispersion-free states, the failure of the…
The new interpretation of Quantum Mechanics is based on a complex probability theory. An interpretation postulate specifies events which can be observed and it follows that the complex probability of such event is, in fact, a real positive…
Quantum computation is a promising emerging technology which, compared to conventional computation, allows for substantial speed-ups e.g. for integer factorization or database search. However, since physical realizations of quantum…
It is proposed the scheme of quantum mechanics, in which a Hilbert space and the linear operators are not primary elements of the theory. Instead of it certain variant of the algebraic approach is considered. The elements of noncommutative…