Related papers: Factor Graphs for Quantum Probabilities
A factor-graph representation of quantum-mechanical probabilities is proposed. Unlike standard statistical models, the proposed representation uses auxiliary variables (state variables) that are not random variables.
The probability representation of states in standard quantum mechanics where the quantum states are associated with fair probability distributions (instead of wave function or density matrix) is shortly commented and bibliography related to…
It is usually believed that a picture of Quantum Mechanics in terms of true probabilities cannot be given due to the uncertainty relations. Here we discuss a tomographic approach to quantum states that leads to a probability representation…
Wigner's marginal probability theory is revisited, and systematically applied to n-particle correlation measurements. A set of Bell inequalities whose corollaries are Hardy contradiction and its generalisation are derived with intuitive…
In prior work, we have shown how the basic concepts and terms of quantum mechanics relate to factorizations and marginals of complex-valued quantum mass functions, which are generalizations of joint probability mass functions. In this…
[...] In this thesis, we are interested in generalizing factor graphs and the relevant methods toward describing quantum systems. Two generalizations of classical graphical models are investigated, namely double-edge factor graphs (DeFGs)…
The form factor of a quantum graph is a function measuring correlations within the spectrum of the graph. It can be expressed as a double sum over the periodic orbits on the graph. We propose a scheme which allows one to evaluate the…
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…
On the base of symplectic quantum tomogram we define a probability distribution on the plane. The dual map transfers all observables which are polynomials of the position and momentum operators to the set of polynomials of two variables. In…
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 review of the tomographic-probability representation of classical and quantum states is presented. The tomographic entropies and entropic uncertainty relations are discussed in connection with ambiguities in the interpretation of the…
A central feature of quantum mechanics is the non-commutativity of operators used to describe physical observables. In this article, we present a critical analysis on the role of non-commutativity in quantum theory, focusing on its…
Quantum graphs are commonly used as models of complex quantum systems, for example molecules, networks of wires, and states of condensed matter. We consider quantum statistics for indistinguishable spinless particles on a graph,…
Is quantum mechanics about 'states'? Or is it basically another kind of probability theory? It is argued that the elementary formalism of quantum mechanics operates as a well-justified alternative to 'classical' instantiations of 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…
These notes are intended as an introduction to a study of applications of noncommutative calculus to quantum statistical Physics. Centered on noncommutative calculus we describe the physical concepts and mathematical structures appearing in…
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 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…
We generalize classical statistical mechanics to describe the kinematics and the dynamics of systems whose variables are constrained by a single quantum postulate (discreteness of the spectrum of values of at least one variable of the…
Concept of entangled probability distribution of several random variables is introduced. These probability distributions describe multimode quantum states in probability representation of quantum mechanics. Example of entangled probability…