Related papers: The spectrogram expansion of Wigner functions
We study the Wigner function for a quantum system with a discrete, infinite dimensional Hilbert space, such as a spinless particle moving on a one dimensional infinite lattice. We discuss the peculiarities of this scenario and of the…
Recent experimental results demonstrated the generation of a quantum superpositon (MQS), involving a number of photons in excess of 5x10^4, which showed a high resilience to losses. In order to perform a complete analysis on the effects of…
I present a novel algorithm for reconstructing the Wigner function from homodyne statistics. The proposed method, based on maximum-likelihood estimation, is capable of compensating for detection losses in a numerically stable way.
It is shown that the Hall, Hu and Marron [Hall, P., Hu, T., and Marron J.S. (1995), Improved Variable Window Kernel Estimates of Probability Densities, {\it Annals of Statistics}, 23, 1--10] modification of Abramson's [Abramson, I. (1982),…
One of the most prominent quasiprobability functions in quantum mechanics is the Wigner function that gives the right marginal probability functions if integrated over position or momentum. Here we depart from the definition of the…
We derive asymptotic expansions of the large zeros of the Coulomb wave functions and for those of their derivatives. The new expansions have the same form as the McMahon expansions of the zeros of the Bessel functions and reduce to them…
In numerous applications data are observed at random times and an estimated graph of the spectral density may be relevant for characterizing and explaining phenomena. By using a wavelet analysis, one derives a nonparametric estimator of the…
The Renyi, Shannon and Fisher spreading lengths of the classical or hypergeometric orthogonal polynomials, which are quantifiers of their distribution all over the orthogonality interval, are defined and investigated. These…
Non-Gaussian quantum states, described by negative valued Wigner functions, are important both for fundamental tests of quantum physics and for emerging quantum information technologies. One of the promising ways of generation of the…
Asymptotic approximations of Jacobi polynomials are given in terms of elementary functions for large degree $n$ and parameters $\alpha$ and $\beta$. From these new results, asymptotic expansions of the zeros are derived and methods are…
We consider properties of the measurement intensity $\rho$ of a random variable for which the probability density function represented by the corresponding Wigner function attains negative values on a part of the domain. We consider a…
Functional data that are nonnegative and have a constrained integral can be considered as samples of one-dimensional density functions. Such data are ubiquitous. Due to the inherent constraints, densities do not live in a vector space and,…
This paper obtains asymptotic results for parametric inference using prediction-based estimating functions when the data are high frequency observations of a diffusion process with an infinite time horizon. Specifically, the data are…
A unification of the set of quasiprobability representations using the mathematical theory of frames was recently developed for quantum systems with finite-dimensional Hilbert spaces, in which it was proven that such representations require…
A number of fundamental quantities in statistical signal processing and information theory can be expressed as integral functions of two probability density functions. Such quantities are called density functionals as they map density…
Photon-number-revolving (PNR) detection allows the direct measurement of the Wigner quasiprobability distribution of an optical mode without the need for numerically processing an inverse Radon transform [K. Banaszek and K. W\'odkiewicz,…
Elliptic partial differential equations with diffusion coefficients of lognormal form, that is $a=exp(b)$, where $b$ is a Gaussian random field, are considered. We study the $\ell^p$ summability properties of the Hermite polynomial…
In the first part of these notes, we review some of the recent developments in the study of the spectral properties of Wigner matrices. In the second part, we present a new proof of a Wegner estimate for the eigenvalues of a large class of…
We obtain a full asymptotic expansion for orthogonal polynomials with respect to weighted area measure on a Jordan domain $\mathscr{D}$ with real-analytic boundary. The weight is fixed and assumed to be real-analytically smooth and strictly…
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…