Related papers: Discrete Wigner functions and the phase space repr…
We show that the number of harmonics of the Wigner function, recently proposed as a measure of quantum complexity, can be also used to characterize quantum phase transitions. The non-analytic behavior of this quantity in the neighborhood of…
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…
The basic idea of quantum computing is surprisingly similar to that of kernel methods in machine learning, namely to efficiently perform computations in an intractably large Hilbert space. In this paper we explore some theoretical…
The central aim of the thesis is to examine how non-classical resources in finite-dimensional quantum systems can be identified, characterized, and protected for practical use in the presence of realistic noise. Using the discrete Wigner…
Time dependence for barrier penetration is considered in the phase space. An asymptotic phase-space propagator for nonrelativistic scattering on a one - dimensional barrier is constructed. The propagator has a form universal for various…
What is the origin of quantum computational advantage? Providing answers to this far-reaching question amounts to identifying the key properties, or quantum resources, that distinguish quantum computers from their classical counterparts,…
It is common knowledge that the Wigner function of a quantum state may admit negative values, so that it cannot be viewed as a genuine probability density. Here, we examine the difficulty in finding an entropy-like functional in phase space…
Within the quantum phase representation we derive Heisenberg limits, in closed form, for N00N states and two other classes of states that can perform better in terms of local performance metrics relevant for multiply-peaked distributions.…
An extension to computational mechanics complexity measure is proposed in order to tackle quantum states complexity quantification. The method is applicable to any $n-$partite state of qudits through some simple modifications. A Werner…
We present the reconstruction of the Wigner function of a classical phase-sensitive state, a pulsed coherent state, by measurements of the distributions of detected-photons of the state displaced by a coherent probe field. By using a hybrid…
We present efficient circuits that can be used for the phase space tomography of quantum states. The circuits evaluate individual values or selected averages of the Wigner, Kirkwood and Husimi distributions. These quantum gate arrays can be…
Conventional quantum computing entails a geometry based on the description of an n-qubit state using 2^{n} infinite precision complex numbers denoting a vector in a Hilbert space. Such numbers are in general uncomputable using any…
We study degenerate three photon down conversion as a potential scheme for generating nonclassical states of light which exhibit clear signatures of phase space interference. The Wigner function representing these states contains an…
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…
A new definition of the Wigner function for quantum fields coupled to curved space--time and an external Yang--Mills field is studied on the example of a scalar and a Dirac fields. The definition uses the formalism of the tangent bundles…
Given a real-valued phase-space function, it is a nontrivial task to determine whether it corresponds to a Wigner distribution for a physically acceptable quantum state. This topic has been of fundamental interest for long, and in a modern…
In this work, we develop a highly efficient representation of functions and differential operators based on Fourier analysis. Using this representation, we create a variational hybrid quantum algorithm to solve static, Schr\"odinger-type,…
Electromagnetic modes are instrumental in building quantum machines. In this experiment, we introduce a method to manipulate these modes by effectively controlling their phase space. Preventing access to a single energy level, corresponding…
Recently a new formulation of quantum mechanics has been suggested which describes systems by means of ensembles of classical particles provided with a sign. This novel approach mainly consists of two steps: the computation of the Wigner…
We discuss questions pertaining to the definition of `momentum', `momentum space', `phase space', and `Wigner distributions'; for finite dimensional quantum systems. For such systems, where traditional concepts of `momenta' established for…