Related papers: Generalized reduction formula for Discrete Wigner …
We propose a phase-space representation concept in terms of the Wigner function for a quantum harmonic oscillator model that exhibits the semiconfinement effect through its mass varying with the position. The new method is used to compute…
We apply reduced density-matrix functional theory to the parabolically confined quantum Hall droplet in the spin-frozen strong magnetic field regime. One-body reduced density matrix functional method performs remarkably well in obtaining…
We first review the usefulness of the Wigner distribution functions (WDF), associated with Lindblad and pre-master equations, for analyzing a host of problems in Quantum Optics where dissipation plays a major role, an arena where weak…
The quantum state of a light beam can be represented as an infinite dimensional density matrix or equivalently as a density on the plane called the Wigner function. We describe quantum tomography as an inverse statistical problem in which…
We further elaborate on a phase-space picture for a system of $N$ qubits and explore the structures compatible with the notion of unbiasedness. These consist of bundles of discrete curves satisfying certain additional properties and…
The Wigner function was introduced as an attempt to describe quantum-mechanical fields with the tools inherited from classical statistical mechanics. In particular, it is widely used to describe the properties of radiation fields. In fact,…
The possibility of constructing a complete, continuous Wigner function for any quantum system has been a subject of investigation for over 50 years. A key system that has served to illustrate the difficulties of this problem has been an…
Recent work [J.S. Lundeen et al. Nature, 474, 188 (2011)] directly measured the wavefunction by weakly measuring a variable followed by a normal (i.e. `strong') measurement of the complementary variable. We generalize this method to mixed…
We present two results on multiqubit Werner states, defined to be those states that are invariant under the collective action of any given single-qubit unitary that acts simultaneously on all the qubits. Motivated by the desire to…
We estimate the quantum state of a light beam from results of quantum homodyne measurements performed on identically prepared quantum systems. The state is represented through the Wigner function, a generalized probability density on…
Taking partial traces for computing reduced density matrices, or related functions, is a ubiquitous procedure in the quantum mechanics of composite systems. In this article, we present a thorough description of this function and analyze the…
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…
General semiclassical expression for quantum fidelity (Loschmidt echo) of arbitrary pure and mixed states is derived. It expresses fidelity as an interference sum of dephasing trajectories weighed by the Wigner function of the initial…
For the visualization of quantum states, the approach based on Wigner functions can be very effective. Homodyne detection has been extensively used to obtain the density matrix, Wigner functions and tomographic reconstructions of optical…
We show that quantum circuits where the initial state and all the following quantum operations can be represented by positive Wigner functions can be classically efficiently simulated. This is true both for continuous-variable as well as…
Quantum tomography has become an indispensable tool in order to compute the density matrix $\rho$ of quantum systems in Physics. Recently, it has further gained importance as a basic step to test entanglement and violation of Bell…
Quantum mechanics can be formulated in terms of phase-space functions, according to Wigner's approach. A generalization of this approach consists in replacing the density operators of the standard formulation with suitable functions, the…
We introduce an efficient method to reconstruct the Wigner function of many-mode continuous variable systems. It is based on convex optimization with semidefinite programs, and also includes a version of the maximum entropy principle, in…
A general approach to obtain reduced models for a wide class of discrete-time quantum systems is proposed. The obtained models not only reproduce exactly the output of a given quantum model, but are also guaranteed to satisfy physical…
A relativistic Wigner function for free Discrete Time Quantum Walks (DTQWs) on the square $2D$ space-time lattice is defined. Useful concepts such as discrete derivatives and discrete distributions are also introduced. The transport…