Related papers: Study on a Phase Space Representation of Quantum T…
A Hermitian quantum phase operator is formulated that mirrors the classical phase variable with proper time dependence and satisfies trigonometric identities. The eigenstates of the phase operator are solved in terms of Gegenbauer…
We introduce a positive phase-space representation for fermions, using the most general possible multi-mode Gaussian operator basis. The representation generalizes previous bosonic quantum phase-space methods to Fermi systems. We derive…
This paper is a continuation of our previous works about coordinate, momentum, dispersion operators and phase space representation of quantum mechanics. It concerns a study on the properties of wavefunctions in the phase space…
The aim of this paper is to present a study on the representations of coordinate, momentum and dispersion operators in the framework of a phase space representation of quantum mechanics that we have introduced and studied in previous works.…
We introduce a unified Gaussian quantum operator representation for fermions and bosons. The representation extends existing phase-space methods to Fermi systems as well as the important case of Fermi-Bose mixtures. It enables simulations…
Phase-space representations are of increasing importance as a viable and successful means to study exponentially complex quantum many-body systems from first principles. This review traces the background of these methods, starting from the…
We introduce matrix quantum phase-space distributions. These extend the idea of a quantum phase-space representation via projections onto a density matrix of global symmetry variables. The method is applied to verification of low-loss…
In this tutorial, we introduce the basic concepts and mathematical tools needed for phase-space description of a very common class of states, whose phase properties are described by Gaussian Wigner functions: the Gaussian states. In…
A Gaussian operator basis provides a means to formulate phase-space simulations of the real- and imaginary-time evolution of quantum systems. Such simulations are guaranteed to be exact while the underlying distribution remains…
We introduce the Gaussian quantum operator representation, using the most general multi-mode Gaussian operator basis. The representation unifies and substantially extends existing phase-space representations of density matrices for Bose…
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…
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…
An adapted representation of quantum mechanics sheds new light on the relationship between quantum states and classical states. In this approach the space of quantum states splits into a product of the state space of classical mechanics and…
We present a detailed discussion of a general theory of phase-space distributions, introduced recently by the authors [J. Phys. A {\bf 31}, L9 (1998)]. This theory provides a unified phase-space formulation of quantum mechanics for physical…
In this work, improvements are introduced to the current models of the ideal Fermi gas and the ideal Bose gas by incorporating the quantum nature of phase space, which is directly linked to the uncertainty principle. These improved models…
A combined method for analyzing quantum dynamical equations which uses the Bohmian mechanics and the quantum phase space representation is proposed. It is based on a presentation of the wave function in phase space in a polar form. The…
We introduce a quantum like representation of a Spiral Phase Plate, acting on an electromagnetic field, as a two mode phase operator. The representation is based on the Newton binomial expansion and on properties of rational power of…
We investigate quasi-hermitian quantum mechanics in phase space using standard deformation quantization methods: Groenewold star products and Wigner transforms. We focus on imaginary Liouville theory as a representative example where exact…
Gaussian states -- or, more generally, Gaussian operators -- play an important role in Quantum Optics and Quantum Information Science, both in discussions about conceptual issues and in practical applications. We describe, in a tutorial…
Gaussian states are at the heart of quantum mechanics and play an essential role in quantum information processing. In this paper we provide approximation formulas for the expansion of a general Gaussian symbol in terms of elementary…