Related papers: Local sampling of the SU(1,1) Wigner function
Previously, an explicit solution for the time evolution of the Wigner function was presented in terms of auxiliary phase space coordinates which obey simple equations that are analogous with, but not identical to, the classical equations of…
Most methods for experimentally reconstructing the quantum state of light involve determining a quasiprobability distribution such as the Wigner function. In this paper we present a scheme for measuring individual density matrix elements in…
In this paper, the ground state Wigner function of a many-body system is explored theoretically and numerically. First, an eigenvalue problem for Wigner function is derived based on the energy operator of the system. The validity of finding…
We formulate, with full generality, the asymptotic estimation theory for Gaussian states in terms of their first and second moments. By expressing the quantum Fisher information (QFI) and the elusive symmetric logarithmic derivative (SLD)…
This dissertation serves as a general introduction to Wigner functions, phase space, and quantum metrology but also strives to be useful as a how-to guide for those who wish to delve into the realm of using continuous variables, to describe…
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…
The Wigner function shares several properties with classical distribution functions on phase space, but is not positive-definite. The integral of the Wigner function over a given region of phase space can therefore lie outside the interval…
Wigner phase space quasi-probability distribution function is a Fourier transform related to a given quantum mechanical wave function. It is shown that for the wave functions of type $\psi (q)=e^{-aq^2}\phi (q)$, the Wigner function can be…
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…
In this work we study symplectic unitary representations for the Galilei group. As a consequence the Schr\"odinger equation is derived in phase space. The formalism is based on the non-commutative structure of the star-product, and using…
Precise modeling of extended sources is a central challenge in modern optical engineering, laser physics, and computational lithography. Unlike ideal point sources or completely incoherent thermal radiation sources, real-world light sources…
Recent electron quantum optics experiments performed with on-demand single electron sources call for a mixed time/frequency approach to electronic quantum coherence. Here, we present a Wigner function representation of first order…
We show that a class of multimode optical transformations that employ linear optics plus two-mode squeezing can be expressed as SU(1,1) operators. These operations are relevant to state-of-the-art continuous variable quantum information…
In this note we generalize the well-known Wigner's unitary-anti\-unitary theorem. For $X$ and $Y$ smooth normed spaces and $f:X\to Y$ a surjective mapping such that $|[f(x),f(y)]|=|[x,y]|$, $x,y\in X$, where $[\cdot,\cdot]$ is the unique…
The representation of quantum states via phase-space functions constitutes an intuitive technique to characterize light. However, the reconstruction of such distributions is challenging as it demands specific types of detectors and detailed…
This paper is concerned with a certain aspect of the spectral theory of unitary operators in a Hilbert space and its aim is to give an explicit construction of continuous functions of unitary operators. Starting from a given unitary…
Compared to passive interferometers, SU(1,1) interferometers exhibit superior phase sensitivity due to the incorporation of nonlinear elements that enhance their ability to detect phase shifts. However, the precision of these…
The Wigner function plays a central role in QCD as a phase space object encoding correlations among quarks, antiquarks, and gluons, yet its interpretation remains subtle due to its quasiprobabilistic nature and possible negativity. Recent…
We derive a quantum version of the classical-optics Wiener-Khintchine theorem within the framework of detection of phase-space displacements with a suitably designed quantum ruler. A phase-pace based quantum mutual coherence function is…
An observer at rest with the expanding universe experiences some extra noise in the quantum vacuum, and so does an accelerated observer in a vacuum at rest (in Minkowski space). The literature mainly focuses on the ideal cases of…