Related papers: The quantum state vector in phase space and Gabor'…
The exact solution of the Lindblad equation with a quadratic Hamiltonian and linear coupling operators was derived within the chord representation, that is, for the Fourier transform of the Wigner function, also known as the characteristic…
By means of a well-grounded mapping scheme linking Schwinger unitary operators and generators of the special unitary group $\mathrm{SU(N)}$, it is possible to establish a self-consistent theoretical framework for finite-dimensional discrete…
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,…
We define the Wigner entropy of a quantum state as the differential Shannon entropy of the Wigner function of the state. This quantity is properly defined only for states that possess a positive Wigner function, which we name…
The Wigner function plays a central role in QCD as a phase space object encoding correlations among quarks, antiquarks, and gluons, yet its interpretation remains subtle due to its quasiprobabilistic nature and possible negativity. Recent…
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…
We consider quantum phase-space dynamics using Wigner's representation of quantum mechanics. We stress the usefulness of the integral form for the description of Wigner's phase-space current~$\bm J$ as an alternative to the popular Moyal…
The quantum state of a system of qubits can be represented by a Wigner function on a discrete phase space, each axis of the phase space taking values in a finite field. Within this framework, we show that one can make sense of the notion of…
Quantum engineering now allows to design and construct multi-qubit states in a range of physical systems. These states are typically quite complex in nature, with disparate, but relevant properties that include both single and multi-qubit…
The theory of quantum propagator and time--dependent integrals of motion in quantum optics is reviewed as well as the properties of Wigner function, Q--function, and coherent state representation. Propagators and wave functions of a free…
We propose a gate-based quantum algorithm for the prediction step of Bayesian state estimation based on the Fokker-Planck equation on a discretized position-velocity state space. The probability density is encoded in the amplitudes of a…
We examine the visualization of quantum mechanics in phase space by means of the Wigner function and the Wigner function flow as a complementary approach to illustrating quantum mechanics in configuration space by wave functions. The Wigner…
We introduce new representations to formulate quantum mechanics on noncommutative phase space, in which both coordinate-coordinate and momentum-momentum are noncommutative. These representations explicitly display entanglement properties…
Generalised Wigner and Weyl transformations of quantum operators are defined and their properties, as well as those of the algebraic structure induced on the phase-space are studied. Using such transformations, quantum linear evolution…
In this second in a series of four articles we create a mathematical formalism sufficient to represent nontrivial hamiltonian quantum dynamics, including resonances. Some parts of this construction are also mathematically necessary. The…
New time dependent Wigner functions for the quantum harmonic oscillator have been obtained in this work. The Moyal equation for the harmonic oscillator has been presented as the wave equation of a 2D membrane in the phase plane. The values…
A two-step optimization is proposed to represent an arbitrary quantum state to a desired accuracy with the least number of gaussians in phase space. The Husimi distribution of the quantum state provides the information to determine the…
Using the Wigner distribution function, we analyze the behavior on phase space of generalized coherent states associated with the Morse potential (Morse-like coherent states). Within the f-deformed oscillator formalism, such states are…
The Projection Postulate from Standard Quantum Mechanics relies fundamentally on measurements. But measurements implicitly suggest the existence of anthropocentric notions like measuring devices, which should rather emerge from the theory.…
Since the very early days of quantum theory there have been numerous attempts to interpret quantum mechanics as a statistical theory. This is equivalent to describing quantum states and ensembles together with their dynamics entirely in…