Related papers: Wigner distributions for finite state systems with…

Beam splitters allow us to superpose two continuous single mode quantum systems. To study the behaviour of their strongly mode mixing dynamics we consider variable beam splitters and their dynamics using Wigner's phase space distribution,…

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…

The randomized quantum marginal problem asks about the joint distribution of the partial traces ("marginals") of a uniform random Hermitian operator with fixed spectrum acting on a space of tensors. We introduce a new approach to this…

The phase-space representation for a relativistic linear oscillator in a homogeneous external field expressed through the finite-difference equation is constructed. Explicit expressions of the relativistic oscillator Wigner…

We study the phase-space concentration of the so-called generalized metaplectic operators whose main examples are Schr\"odinger equations with bounded perturbations. To reach this goal, we perform a so-called $\mathcal{A}$-Wigner analysis…

Starting from the Pauli Hamiltonian operator, we derive a scalar quantum kinetic equations for spin-1/2 systems. Here the regular Wigner two-state matrix is replaced by a scalar distribution function in extended phase space. Apart from…

Wigner distributions play a significant role in formulating the phase space analogue of quantum mechanics. The Schrodinger wave-functional for solitons is needed to derive it for solitons. The Wigner distribution derived can further be used…

Phase-space representations based on coherent states (P, Q, Wigner) have been successful in the creation of stochastic differential equations (SDEs) for the efficient stochastic simulation of high dimensional quantum systems. However many…

We present a phase space description of the process of quantum teleportation for a system with an $N$ dimensional space of states. For this purpose we define a discrete Wigner function which is a minor variation of previously existing ones.…

In continuous-variable quantum computation, identifying key elements that enable a quantum computational advantage is a long-standing issue. Starting from the standard results on the necessity of Wigner negativity, we develop a…

We analyse some features of the class of discrete Wigner functions that was recently introduced by Gibbons et al. to represent quantum states of systems with power-of-prime dimensional Hilbert spaces [Phys. Rev. A 70, 062101 (2004)]. We…

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…

We present a self-consistent theoretical framework for finite-dimensional discrete phase spaces that leads us to establish a well-grounded mapping scheme between Schwinger unitary operators and generators of the special unitary group…

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…

In this article we introduce a novel quantum state, the perfect quantum optical vortex state which exhibits a highly localised distribution along a ring in the quadrature space. We examine its nonclassical properties using the Wigner…

The general Weyl -- Wigner formalism in finite dimensional phase spaces is investigated. Then this formalism is specified to the case of symmetric ordering of operators in an odd -- dimensional Hilbert space. A respective Wigner function on…

In this paper, we consider the quantum-mechanical phase space patterns on ordered and disordered networks. For ordered networks in which each node is connected to its 2m nearest neighbors (m on either side), the phase space…

We consider Schr\"{o}dinger equations with real quadratic Hamiltonians, for which the Wigner distribution of the solution at a given time equals, up to a linear coordinate transformation, the Wigner distribution of the initial condition.…

Metaplectic Wigner distributions were recently investigated as natural generalizations of the classical Wigner distribution, and provide a wide class of time-frequency representations that exploits the structure of the symplectic group.…

The Wigner function is a well-known phase space distribution function with many applications in quantum mechanics. In this article, we consider an open quantum system consisting of a non-relativistic single particle interacting with a…