Related papers: Wigner entropy conjecture and the interference for…
We have considered optical beams with phase singularity and experimentally verified that these beams, although being classical, have properties of two mode entanglement in quantum states. We have observed the violation of Bell's inequality…
We provide a detailed description of the EPR paradox (in the Bohm version) for a two qubit-state in the discrete Wigner function formalism. We compare the probability distributions for two qubit relevant to simultaneously-measurable…
Wigner phase space quasi-probability distribution function is a Fourier transform related to a given quantum mechanical wave function. It is shown that for the wave functions of type $\psi (q)=e^{-aq^2}\phi (q)$, the Wigner function can be…
For an ergodic system, the time average of a classical observable coincides with that obtained via the Liouville probability density, a delta-function on the energy shell. Reinterpreting this distribution as a Wigner function, that is, the…
A gauge-invariant Wigner quantum mechanical theory is obtained by applying the Weyl-Stratonovich transform to the von Neumann equation for the density matrix. The transform reduces to the Weyl transform in the electrostatic limit, when the…
The phase-space formulation of quantum mechanics has recently seen increased use in testing quantum technologies, including metho ds of tomography for state verification and device validation. Here, an overview of quantum mechanics in phase…
We study a generalization of the Wigner function to arbitrary tuples of hermitian operators, which is a distribution uniquely characterized by the property that the marginals for all linear combinations of the given operators agree with the…
We propose a very simple experimental setup to measure, via photon counting, the overlap of the Wigner functions characterizing two single mode light beams. We show that this scheme can be applied to determine directly the phase space…
We construct a complete set of Wannier functions which are localized at both given positions and momenta. This allows us to introduce the quantum phase space, onto which a quantum pure state can be mapped unitarily. Using its probability…
Phase-space representations as given by Wigner functions are a powerful tool for representing the quantum state and characterizing its time evolution in the case of infinite-dimensional quantum systems and have been widely used in quantum…
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 demonstrate that the Wigner function of the Einstein-Podolsky-Rosen state, though positive definite, provides a direct evidence of the nonlocal character of this state. The proof is based on an observation that the Wigner function…
General semiclassical expression for quantum fidelity (Loschmidt echo) of arbitrary pure and mixed states is derived. It expresses fidelity as an interference sum of dephasing trajectories weighed by the Wigner function of the initial…
The Wigner function W(q,p) is formulated as a phase-space path integral, whereby its sign oscillations can be seen to follow from interference between the geometrical phases of the paths. The approach has similarities to the path-centroid…
We study the ground state of a system of spinless electrons interacting through a screened Coulomb potential in a lattice ring. By using analytical arguments, we show that, when the effective interaction compares with the kinetic energy,…
We examine the interpretation of individual phase-space trajectories of the Wigner function as corresponding to possible outcomes of single experimental trials. To this end, we investigate the relation between the true (measured) particle…
Polarization quasiprobability distribution defined in the Stokes space shares many important properties with the Wigner function for the position and momentum. Most notably, they both give correct one-dimensional marginal probability…
Generation of Wigner functions of Landau levels and determination of their symmetries and generic properties are achieved in the autonomous framework of deformation quantization. Transformation properties of diagonal Wigner functions under…
Transition from quantum to semiclassical behaviour and loss of quantum coherence for inhomogeneous perturbations generated from a non-vacuum initial state in the early Universe is considered in the Heisenberg and the Schr\"odinger…
Phase space reflection operators lie at the core of the Wigner-Weyl representation of density operators and observables. The role of the corresponding classical reflections is known in the construction of semiclassical approximations to…