Related papers: Multidimensional Hermite polynomials and photon di…
We present a calculation of the generalized parton distributions of the photon using overlaps of photon light-front wave functions.
This paper presents the construction of a new set of generalized photon-added coherent states related to associated hypergeometric functions introduced in our previous work (Hounkonnou M N and Sodoga K, 2005, J. Phys. A: Math. Gen 38,…
Propagating modes of light with negative-valued Wigner distributions are of fundamental interest in quantum optics and represent a key resource in the pursuit of optics-based quantum information technologies. Most schemes proposed or…
Higher (2nd)-order Wigner distribution function in quantum phase space for entangled bi-modal coherent states, a representative of higher (2nd)-order optical-polarization, is introduced by generalizing kernel (transiting) operator in…
We have studied theoretical un-symmetric multi-photon subtracted twin beam state and demonstrated a method for generating states that resembles to high photon number states with the increase in the number of subtracted photons through…
It is shown that a highly phase sensitive polarization squeezed (2n-1)-photon state can be generated by subtracting a diagonally polarized photon from the 2n photon component generated in collinear type II downconversion. This polarization…
Wigner functions generically attain negative values and hence are not probability densities. We prove an asymptotic expansion of Wigner functions in terms of Hermite spectrograms, which are probability densities. The expansion provides…
Gaussian distributions can be generalized from Euclidean space to a wide class of Riemannian manifolds. Gaussian distributions on manifolds are harder to make use of in applications since the normalisation factors, which we will refer to as…
Generalizing previous work of Hora (1998) on the asymptotic spectral analysis for the Hamming graph $H(n,q)$ which is the $n^{\mathrm{th}}$ Cartesian power $K_q^{\square n}$ of the complete graph $K_q$ on $q$ vertices, we describe the…
This paper investigates the combinatorics that gives rise to the Boltzmann probability distribution. Despite being one of the most important distributions in physics and other fields of science, the mathematics of the underlying model of…
The photon density operator function is used to calculate light beam propagation through turbulent atmosphere. A kinetic equation for the photon distribution function is derived and solved using the method of characteristics. Optical wave…
A scheme for conditional generating a Hermite polynomial excited squeezed vacuum states (HESVS) is proposed. Injecting a two-mode squeezed vacuum state (TMSVS) into a beam splitter (BS) and counting the photons in one of the output…
The spectra and generalized eigenfunctions of the hyperbolic and parabolic generators of the standard representation of SU(1,1) in the one-mode boson Hilbert space are derived. The eigenfunctions are given in three different forms,…
This paper introduces a new generalized polynomial chaos expansion (PCE) comprising multivariate Hermite orthogonal polynomials in dependent Gaussian random variables. The second-moment properties of Hermite polynomials reveal a weakly…
The continuing improvement in the qualities of photon-number-resolving detectors opens new possibilities for measuring quantum states of light. In this work we consider the question of what properties of an arbitrary multimode Gaussian…
We study the Wigner functions of the nucleon which provide multidimensional images of the quark distributions in phase space and combine in a single picture all the information contained in the generalized parton distributions (GPDs) and…
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…
Let $G$ be a finite connected graph on two or more vertices and $G^{[N,k]}$ the distance $k$-graph of the $N$-fold Cartesian power of $G$. For a fixed $k\ge1$, we obtain explicitly the large $N$ limit of the spectral distribution (the…
We show that the Riemannian Gaussian distributions on symmetric spaces, introduced in recent years, are of standard random matrix type. We exploit this to compute analytically marginals of the probability density functions. This can be done…
We present a calculation of the generalized parton distributions of the photon when there is non-zero momentum transfer both in the transverse and longitudinal directions. We consider only the contributions when the photon helicity is not…