相关论文: Area Potentials and Deformation Quantization
We consider the time-independent Wigner functions of phase-space quantum mechanics (a.k.a. deformation quantization) for a Morse potential. First, we find them by solving the $\ast$-eigenvalue equations, using a method that can be applied…
We review the Weyl-Wigner formulation of quantum mechanics in phase space. We discuss the concept of Narcowich-Wigner spectrum and use it to state necessary and sufficient conditions for a phase space function to be a Wigner distribution.…
We show that the behaviour in phase space of the Wigner function associated to the electromagnetic modes carries the information of both, the entanglement properties between matter and field, and the regions in parameter space where quantum…
Focusing particularly on one-qubit and two-qubit systems, I explain how the quantum state of a system of n qubits can be expressed as a real function--a generalized Wigner function--on a discrete 2^n x 2^n phase space. The phase space is…
To quantify the effect of decoherence in quantum measurements, it is desirable to measure not merely the square modulus of the spatial wavefunction, but the entire density matrix, whose phases carry information about momentum and how pure…
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…
Deformation quantization is applied to quantize gravitational systems coupled with matter. This quantization procedure is performed explicitly for quantum cosmology of these systems in a flat minisuper(phase)space. The procedure is employed…
Wigner's quasi-probability distribution function in phase-space is a special (Weyl) representation of the density matrix. It has been useful in describing quantum transport in quantum optics; nuclear physics; decoherence (eg, quantum…
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…
Quantum devices are preparing increasingly more complex entangled quantum states. How can one effectively study these states in light of their increasing dimensions? Phase spaces such as Wigner functions provide a suitable framework. We…
In order to quantize systems involving second-class constraints, one should use Dirac bracket instead of Poisson bracket. Furthermore, one can specify a star product in which the term linear in $\hbar$ is proportional to the Dirac bracket.…
The original Wigner function provides a way of representing in phase space the quantum states of systems with continuous degrees of freedom. Wigner functions have also been developed for discrete quantum systems, one popular version being…
Second quantization of a classical nonrelativistic one-particle system as a deformation quantization of the Schrodinger spinless field is considered. Under the assumption that the phase space of the Schrodinger field is $C^{\infty}$, both,…
The Wigner function for one and two-mode quantum systems is explicitely expressed in terms of the marginal distribution for the generic linearly transformed quadratures. Then, also the density operator of those systems is written in terms…
Classical surfaces in phase space correspond to quantum states in Hilbert space. Subsystems specify factor spaces of the Hilbert space. An entangled state corresponds semiclassically to a surface that cannot be decomposed into a product of…
The paper develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical…
A discussion of discrete Wigner functions in phase space related to mutually unbiased bases is presented. This approach requires mathematical assumptions which limits it to systems with density matrices defined on complex Hilbert spaces of…
The need to retain the relative phases in quantum mechanics implies an addition law parametrized by a phase of two density operators required for the purification of a density matrix. This is shown with quantum tomography and the Wigner…
The deformation quantization formalism is applied to the linearized gravitational field. Standard aspects of this formalism are worked out before the ground state Wigner functional is obtained. Finally, the propagator for the graviton is…
Deformation quantization is a powerful tool to quantize some classical systems especially in noncommutative space. In this work we first show that for a class of special Hamiltonian one can easily find relevant time evolution functions and…