Related papers: Wigner function and the probability representation…
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 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,…
Using the remarkable mathematical construct of Eugene Wigner to visualize quantum trajectories in phase space, quantum processes can be described in terms of a quasi-probability distribution analogous to the phase space probability…
We estimate the quantum state of a light beam from results of quantum homodyne measurements performed on identically prepared quantum systems. The state is represented through the Wigner function, a generalized probability density on…
The Wigner distribution function is a quasi-probability distribution. When properly integrated, it provides the correct charge and current densities, but it gives negative probabilities in some points and regions of the phase space.…
We have found an effective method of calculating the Wigner function, being a quantum analogue of joint probability distribution of position and momentum, for bound states of nonrelativistic hydrogen atom. The formal similarity between the…
We present a new quasi-probability distribution function for ensembles of spin-half particles or qubits that has many properties in common with Wigner's original function for systems of continuous variables. We show that this function…
The linear canonical transforms of position and momentum are used to construct the tomographic probability representation of quantum states where the fair probability distribution determines the quantum state instead of the wave function or…
The tomographic probability distribution is used to decribe the kinetic equations for open quantum systems. Damped oscillator is studied. Purity parameter evolution for different damping regime is considered.
The effect of random shooting of particles is considered on the basis of solution of the Schrodinger equation and in terms of the Wigner function. Two-particles description shows, in particular, that initial correlation leads to high…
We study an application of the quantum tomography framework for the time-frequency analysis of modulated signals. In particular, we calculate optical tomographic representations and Wigner-Ville distributions for signals with amplitude and…
Wigner functions provide a way to do quantum physics using quasiprobabilities, that is, "probability" distributions that can go negative. Informationally complete POVMs, a much younger subject than phase space formulations of quantum…
We extend the Wigner-Weyl-Moyal phase-space formulation of quantum mechanics to general curved configuration spaces. The underlying phase space is based on the chosen coordinates of the manifold and their canonically conjugate momenta. The…
The interconnection between quantum mechanics and probabilistic classical mechanics for a free relativistic particle is derived in terms of Wigner functions (WF) for both Dirac and Klein-Gordon (K-G) equations. Construction of WF is…
The method of constructing the tomographic probability distributions describing quantum states in parallel with density operators is presented. Known examples of Husimi-Kano quasi-distribution and photon number tomography are reconsidered…
A gauge-invariant Wigner quasi-distribution function for charged particles in classical electromagnetic fields is derived in a rigorous way. Its relation to the axial gauge is discussed, as well as the relation between the kinetic and…
The Wigner quasiprobability distribution of a narrowband single-photon state was reconstructed by quantum state tomography using photon-number-resolving measurements with transition-edge sensors (TES) at system efficiency 58(2)%. This…
The new inequality recently found by Trifonov and called the state-extended inequality is considered in the tomographic-probability representation of quantum mechanics. The Trifonov uncertainty relations are expressed in terms of optical…
In this paper we study the quantum cosmology of homogeneous and isotropic cosmology, via the Weyl-Wigner-Groenewold-Moyal formalism of phase space quantization, with perfect fluid as a matter source. The corresponding quantum cosmology is…
We represent both the states and the evolution of a quantum computer in phase space using the discrete Wigner function. We study properties of the phase space representation of quantum algorithms: apart from analyzing important examples,…