Related papers: Properties of the Wigner distribution for n arbitr…
We study a generalization of the Wigner function to arbitrary tuples of hermitian operators. We show that for any collection of hermitian operators A1...An , and any quantum state there is a unique joint distribution on R^n, with the…
In this article we introduce a quasiprobability distribution of work that is based on the Wigner function. This construction rests on the idea that the work done on an isolated system can be coherently measured by coupling the system to a…
The probability distribution for finding a state of the radiation field in a particular phase is described by a multitude of theoretical formalisms; the phase-sensitivity of the Wigner quasi-probability distribution being one of them. We…
A class of signed joint probability measures for n arbitrary quantum observables is derived and studied based on quasi-characteristic functions with symmetrized operator orderings of Margenau-Hill type. It is shown that the Wigner…
We define a Wigner distribution function for a one-dimensional finite quantum system, in which the position and momentum operators have a finite (multiplicity-free) spectrum. The distribution function is thus defined on discrete…
This paper aims to explore the inherent connection among Heisenberg groups, quantum Fourier transform and (quasiprobability) distribution functions. Distribution functions for continuous and finite quantum systems are examined first as a…
We develop the theory of Wigner representations for general probabilistic theories (GPTs), a large class of operational theories that include both classical and quantum theory. The Wigner representations that we introduce are a natural way…
Husimi distributions and Wigner distributions are well-known quasi-probability distributions which appear in several contexts. In this paper, we show some remarkable aspects of these distribution functions related to geometric structures of…
The Wigner function for one and two-mode quantum systems is explicitely expressed in terms of the marginal distribution for the generic linearly transformed quadratures. Then, also the density operator of those systems is written in terms…
Measurement incompatibility and the negativity of quasiprobability distribution functions are well-known non-classical aspects of quantum systems. Both of them are widely accepted resources in quantum information processing. We acquaint an…
We consider the problem of setting up the Wigner distribution for states of a quantum system whose configuration space is a Lie group. The basic properties of Wigner distributions in the familiar Cartesian case are systematically…
The Wigner function of quantum systems is an effective instrument to construct the approximate classical description of the systems for which the classical approximation is possible. During the last time, the Wigner function formalism is…
Wigner distributions for quantum mechanical systems whose configuration space is a finite group of odd order are defined so that they correctly reproduce the marginals and have desirable transformation properties under left and right…
The integral of the Wigner function over a subregion of the phase-space of a quantum system may be less than zero or greater than one. It is shown that for systems with one degree of freedom, the problem of determining the best possible…
The review of star-product formalism providing the possibility to describe quantum states and quantum observables by means of the functions called symbols of operators which are obtained by means of bijective maps of the operators acting in…
One of the most prominent quasiprobability functions in quantum mechanics is the Wigner function that gives the right marginal probability functions if integrated over position or momentum. Here we depart from the definition of the…
In contrast to classical physics, the language of quantum mechanics involves operators and wave functions (or, more generally, density operators). However, in 1932, Wigner formulated quantum mechanics in terms of a distribution function…
We study the properties of the discrete Wigner distribution for two qubits introduced by Wotters. In particular, we analyze the entanglement properties within the Wigner distribution picture by considering the negativity of the Wigner…
The Wigner function, which provides a phase-space description of quantum systems, has various applications in quantum mechanics, quantum kinetic theory, quantum optics, radiation transport and others. The concept of Wigner function has been…
Metaplectic Wigner distributions were recently investigated as natural generalizations of the classical Wigner distribution, and provide a wide class of time-frequency representations that exploits the structure of the symplectic group.…