Related papers: Wigner negativity, random matrices and gravity

Using the remarkable mathematical construct of Eugene Wigner to visualize quantum trajectories in phase space, quantum processes can be described in terms of a quasi-probability distribution analogous to the phase space probability…

We derive an analytical expression of a Wigner function that approximately describes the time evolution of the one-dimensional motion of a particle in a nonharmonic potential. Our method involves two exact frame transformations, accounting…

We quantify the quantum-to-classical transition of the single-mode Kerr nonlinear dynamics in the presence of loss. We establish three time scales that govern the dynamics, each with distinct characteristics. For times short compared to the…

We introduce an operational criterion to identify Wigner function (WF) negativity for an arbitrary quantum state within the framework of quantum non-demolition measurements. This criterion corresponds to experimentally accessible schemes…

The Wigner function's behavior of accelerated and non-accelerated Greenberger Horne Zeilinger (GHZ) state is discussed. For the non-accelerated GHZ state, the minimum/maximum peaks of the Wigner function depends on the distribution's…

The Wigner function formalism has played a pivotal role in examining the non-classical aspects of quantum states and their classical simulatability. Nevertheless, its application in qubit systems faces limitations due to negativity induced…

The presence of unique quantum correlations is the core of quantum information processing and general quantum theory. We address the fundamental question of how quantum correlations of a generic quantum system can be probed using…

A new non-perturbative approach to quantum theory in curved spacetime and to quantum gravity, based on a generalisation of the Wigner equation, is proposed. Our definition for a Wigner equation differs from what have otherwise been…

We demonstrate that the Wigner function of a pure quantum state is a wave function in a specially tuned Dirac bra-ket formalism and argue that the Wigner function is in fact a probability amplitude for the quantum particle to be at a…

Spread complexity uses the distribution of support of a time-evolving state in the Krylov basis to quantify dispersal across accessible dimensions of a Hilbert space. Here, we describe how variations in initial conditions, the Hamiltonian,…

A measure of nonclassicality of quantum states based on the volume of the negative part of the Wigner function is proposed. We analyze this quantity for Fock states, squeezed displaced Fock states and cat-like states defined as coherent…

I investigate the propagator of the Wigner function for a dissipative chaotic quantum map. I show that a small amount of dissipation reduces the propagator of sufficiently smooth Wigner functions to its classical counterpart, the…

Over decades, the time evolution of Wigner functions along classical Hamiltonian flows has been used for approximating key signatures of molecular quantum systems. Such approximations are for example the Wigner phase space method, the…

In [Phys. Rev. A 70, 062101 (2004)] Gibbons et al. defined a class of discrete Wigner functions W to represent quantum states in a finite Hilbert space dimension d. I characterize a set C_d of states having non-negative W simultaneously in…

We study the time evolution of the reduced Wigner function for a class of quantum Brownian motion models. We derive two generalized uncertainty relations. The first consists of a sharp lower bound on the uncertainty function, $U = (\Delta…

Krylov complexity provides a powerful framework for characterizing the dynamical evolution of quantum systems through the spreading of states in Krylov space. The motivation for this is rooted in the optimality of the Krylov basis for the…

The emergence of classical behavior from quantum mechanics as Planck's constant $\hbar$ approaches zero remains a fundamental challenge in physics [1-3]. This paper introduces a novel approach employing deep neural networks to directly…

By means of studying the evolution equation for the Wigner distributions of quantum dissipative systems we derive the quantum corrections to the classical Liouville dynamics, taking into account the standard quantum friction model. The…

Krylov complexity measures the spread of the wavefunction in the Krylov basis, which is constructed using the Hamiltonian and an initial state. We investigate the evolution of the maximally entangled state in the Krylov basis for both…

The Wigner function is a useful tool for exploring the transition between quantum and classical dynamics, as well as the behavior of quantum chaotic systems. Evolving the Wigner function for open systems has proved challenging however; a…