Related papers: Discrete phase space based on finite fields
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…
We develop a path integral representation for the dynamics of quantum systems with a finite-dimensional Hilbert space, formulated entirely within a discrete phase space. Starting from the discrete Wigner function defined on $\mathbb{Z}_d…
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…
We propose a method for classical simulation of finite-dimensional quantum systems, based on sampling from a quasiprobability distribution, i.e., a generalized Wigner function. Our construction applies to all finite dimensions, with the…
The evolution of the discrete Wigner function is formally similar to a probabilistic process, but the transition probabilities, like the discrete Wigner function itself, can be negative. We investigate these transition probabilities, as…
We put forward a method of constructing discrete coherent states for n qubits. After establishing appropriate displacement operators, the coherent states appear as displaced versions of a fiducial vector that is fixed by imposing a number…
The Gibbs canonical state, as a maximum entropy density matrix, represents a quantum system in equilibrium with a thermostat. This state plays an essential role in thermodynamics and serves as the initial condition for nonequilibrium…
In this thesis concrete quantum systems are investigated in the framework of the environment induced decoherence. The focus is on the dynamics of highly nonclassical quantum states, the Wigner function of which are negative over some…
The Wigner function formalism has been applied to the analysis of elastic scattering processes. The new element of known formalism is the choice of the phase space on which the Wigner function is defined. This phase space is 4-dimensional…
In this paper, a gradient flow model is proposed for conducting ground state calculations in Wigner formalism of many-body system in the framework of density functional theory. More specifically, an energy functional for the ground state in…
The Wigner function of quantum systems is an effective instrument to construct the approximate classical description of the systems for which the classical approximation is possible. During the last time, the Wigner function formalism is…
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…
In the usual formulation of quantum mechanics, groups of automorphisms of quantum states have ray representations by unitary and antiunitary operators on complex Hilbert space, in accordance with Wigner's Theorem. In the phase-space…
The concept of phase space amplitudes for systems with continuous degrees of freedom is generalized to finite-dimensional spin systems. Complex amplitudes are obtained on both a sphere and a finite lattice, in each case enabling a more…
While commonly used entanglement criteria for continuous variable systems are based on quadrature measurements, here we study entanglement detection from measurements of the Wigner function. These are routinely performed in platforms such…
The quantum systems with finite-dimensional Hilbert space have several applications and are intensively explored theoretically and experimentally. The mathematical description of these systems follows the analogy with the usual…
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.…
The Weyl-Wigner-Moyal formalism for quantum particle with discrete internal degrees of freedom is developed. A one to one correspondence between operators in the Hilbert space $L^{2}(\mathbb{R}^{3})\otimes{\mathcal{H}}^{(s+1)}$ and…
In quantum resource theory, one is often interested in identifying which states serve as the best resources for particular quantum tasks. If a relative comparison between quantum states can be made, this gives rise to a partial order, where…
Forty-five years after the point de d\'epart [1] of density functional theory, its applications in chemistry and the study of electronic structures keep steadily growing. However, the precise form of the energy functional in terms of the…