Related papers: Integral-free Wigner functions
Exploring the analogy between quantum mechanics and statistical mechanics we formulate an integrated version of the Quantropy functional [1]. With this prescription we compute the propagator associated to Boltzmann-Gibbs statistics in the…
We examine the weak quantum noise limit of Wigner equation for phase space distribution functions. It has been shown that the leading order quantum noise described in terms of an auxiliary Hamiltonian manifests itself as an additional…
We present an operational definition of the Wigner function. Our method relies on the Fresnel transform of measured Rabi oscillations and applies to motional states of trapped atoms as well as to field states in cavities. We illustrate this…
Quantum information is a common topic of research in many areas of quantum physics, such as quantum communication and quantum computation, as well as quantum thermodynamics. It can be encoded in discrete or continuous variable systems, with…
Drawing inspiration from Dirac's work on functions of non commuting observables, we develop a fresh approach to phase space descriptions of operators and the Wigner distribution in quantum mechanics. The construction presented here is…
The Heisenberg evolution of a given unitary operator corresponds classically to a fixed canonical transformation that is viewed through a moving coordinate system. The operators that form the bases of the Weyl representation and its Fourier…
The Wigner function is a phase space quasi-probability distribution whose negative regions provide a direct, local signature of nonclassicality. To identify where phase-sensitive structure concentrates, we introduce local positive- and…
This article outlines a novel interpretation of quantum theory: the Q-based interpretation. The core idea underlying this interpretation, recently suggested for quantum field theories by Drummond and Reid [2020], is to interpret the phase…
The relation of the Wigner function with the fair probability distribution called tomographic distribution or quantum tomogram associated with the quantum state is reviewed. The connection of the tomographic picture of quantum mechanics…
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…
We investigate quantum tunneling in smooth symmetric and asymmetric double-well potentials. Exact solutions for the ground and first excited states are used to study the dynamics. We introduce Wigner's quasi-probability distribution…
We show that the de Broglie-Bohm interpretation can be easily implemented in quantum phase space through the method of quasi-distributions. This method establishes a connection with the formalism of the Wigner function. As a by-product, we…
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…
Given a real-valued phase-space function, it is a nontrivial task to determine whether it corresponds to a Wigner distribution for a physically acceptable quantum state. This topic has been of fundamental interest for long, and in a modern…
We study the Wigner functions of the nucleon which provide multidimensional images of the quark distributions in phase space and combine in a single picture all the information contained in the generalized parton distributions (GPDs) and…
In the present paper a method of finding the dynamics of the Wigner function of a particle in an infinite quantum well is developed. Starting with the problem of a reflection from an impenetrable wall, the obtained solution is then…
We present a quantum theory of the shuttle instability in electronic transport through a nanostructure with a mechanical degree of freedom. A phase space formulation in terms of the Wigner function allows us to identify a cross-over from…
We study the efficiency of quantum algorithms which aim at obtaining phase space distribution functions of quantum systems. Wigner and Husimi functions are considered. Different quantum algorithms are envisioned to build these functions,…
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 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…