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A quantum state can be written in phase space, but the resulting object is not generally the probability density of a positive stochastic process on ordinary phase space. We spell this out for Wigner dynamics. If a positive phase-space…
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 distribution of electromagnetic fields presents a statistical assembly of a particular type, which is at scale h a quantum statistical assembly itself and has also been instrumental to concretisation of the basic probability assumption of…
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 quantum analog of the joint probability distributions describing a classical stochastic process is introduced. A prescription is given for constructing the quantum distribution associated with a sequence of measurements. For the case of…
In this work, we consider the phase-space picture of quantum mechanics. We then introduce non-negative Wigner-like (operational) distributions \widetilde{\mathcal W}_{rho;alpha}(x,p) corresponding to the density operator \hat{rho} and being…
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…
We have reconstructed the quantum state of optical pulses containing single photons using the method of phase-randomized pulsed optical homodyne tomography. The single-photon Fock state |1> was prepared using conditional measurements on…
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…
We investigate the capabilities of loss-tolerant quantum state characterization using a photon-number resolving, time-multiplexed detector (TMD). We employ the idea of probing the Wigner function point-by-point in phase space via photon…
Within the framework of the probability representation of quantum mechanics, we study a superposition of generic Gaussian states associated to symmetries of a regular polygon of n sides; in other words, the cyclic groups (containing the…
A phase space formulation of the filtering process upon an incident quantum state is developed. This formulation can explain the results of both quantum interference and delayed-choice experiments without making use of the controversial…
For the visualization of quantum states, the approach based on Wigner functions can be very effective. Homodyne detection has been extensively used to obtain the density matrix, Wigner functions and tomographic reconstructions of optical…
We investigate features of the quasi-joint-probability distribution for finite-state quantum systems, especially the two-state and three-state quantum systems, comparing different types of quasi-joint-probability distributions based on the…
Free-space propagation can be described as a shearing of the Wigner distribution function in the spatial coordinate; this shearing is linear in paraxial approximation but assumes a more complex shape for wide-angle propagation. Integration…
Representations of the Poincar\'{e} symmetry are studied by using a Hilbert space with a phase space content. The states are described by wave functions ( quasi amplitudes of probability) associated with Wigner functions (quasi probability…
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 study different techniques that allow us to gain complete knowledge about an unknown quantum state, e.g. to perform full tomography of this state. We focus on two apparently simple cases, full tomography of one and two qubit systems. We…
The recently proposed scheme for direct sampling of the quantum phase space by photon counting is discussed within the Wigner function formalism.
The phase-space quasi-probability distribution formalism for representing quantum states provides practical tools for various applications in quantum optics such as identifying the nonclassicality of quantum states. We study filter…