Related papers: Beyond the Standard "Marginalizations" of Wigner F…
Wigner function is a quasi-distribution that provides a representation of the state of a quantum mechanical system in the phase space of position and momentum. In this paper we find a relation between Wigner function and appropriate…
Introduced recently approach based on tomographic probability distribution of quantum states is shown to be closely related with the known notion of the quantum probability measures discussed in quantum information theory and positive…
Starting from the famous Pauli problem on the possibility to associate quantum states with probabilities, the formulation of quantum mechanics in which quantum states are described by fair probability distributions (tomograms, i.e.…
In this note we aim to characterize the cylindrical Wigner measures associated to regular quantum states in the Weyl C*-algebra of canonical commutation relations. In particular, we provide conditions at the quantum level sufficient to…
We propose a phase-space representation concept in terms of the Wigner function for a quantum harmonic oscillator model that exhibits the semiconfinement effect through its mass varying with the position. The new method is used to compute…
We study the Wigner function for the inflationary tensor perturbation defined in the real phase space. We compute explicitly the Wigner function including the contributions from the cubic self-interaction Hamiltonian of tensor…
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 aim of this work is to estimate a quadratic functional of a unknown Wigner function from noisy tomographic data. The Wigner function can be seen as the representation of the quantum state of a light beam. The estimation of a quadratic…
We analyze two two-mode continuous variable separable states with the same marginal states. We adopt the definition of classicality in the form of well-defined positive Wigner function describing the state and find that although the states…
The theory of generalised measurements is used to examine the problem of discriminating unambiguously between non-orthogonal pure quantum states. Measurements of this type never give erroneous results, although, in general, there will be a…
Quantum state tomography is the task of inferring the state of a quantum system by appropriate measurements. Since the frequency distributions of the outcomes of any finite number of measurements will generally deviate from their asymptotic…
We show that the behaviour in phase space of the Wigner function associated to the electromagnetic modes carries the information of both, the entanglement properties between matter and field, and the regions in parameter space where quantum…
We show that the quantum wavefunction, interpreted as the probability density of finding a single non-localized quantum particle, which evolves according to classical laws of motion, is an intermediate description of a material quantum…
The properties of an alternative definition of quantum entropy, based on Wigner functions, are discussed. Such definition emerges naturally from the Wigner representation of quantum mechanics, and can easily quantify the amount of…
The Wigner function was introduced as an attempt to describe quantum-mechanical fields with the tools inherited from classical statistical mechanics. In particular, it is widely used to describe the properties of radiation fields. In fact,…
Quantum state tomography is a key process in most quantum experiments. In this work, we employ quantum machine learning for state tomography. Given an unknown quantum state, it can be learned by maximizing the fidelity between the output of…
The Wigner-Weyl- Moyal approach to Quantum Mechanics is recalled, and similarities to classical probability theory emphasised. The Wigner distribution function is generalised and viewed as a construction of a bosonic object, a target space…
The new numerical version of the Wigner approach to quantum mechanics for treatment thermodynamic properties of strongly coupled systems of particles has been developed for extreme conditions, when analytical approximations obtained in…
An elementary introduction is provided to the phase space quantization method of Moyal and Wigner. We generalize the method so that it applies to 2-dimensional surfaces, where it has an interesting connection with quantum holography. In the…
Probability representation entropy (tomographic entropy) of arbitrary quantum state is introduced. Using the properties of spin tomogram to be standard probability distribution function the tomographic entropy notion is discussed. Relation…