Related papers: Photon distributions and information nonnegativity…
For one-mode light described by the Wigner function of generic Gaussian form the photon distribution function is obtained explicitly and expressed in terms of Hermite polynomials of two variables.The mean values and dispersions of photon…
Uncertainty relation for photons that overcomes the difficulties caused by the nonexistence of the photon position operator is derived in quantum electrodynamics. The photon energy density plays the role of the probability density in…
The review of the following results of the Refs. \cite{Sem} - \cite{Ans} is presented: For mixed state light of $N$-mode electromagnetic field described by Wigner function which has generic Gaussian form the photon distribution function is…
The photon distribution function of a discrete series of excitations of squeezed coherent states is given explicitly in terms of Hermite polynomials of two variables. The Wigner and the coherent-state quasiprobabilities are also presented…
For N-mode light described by the Wigner function of generic Gaussian form the photon distribution function is obtained explicitly and expressed in terms of Hermite polynomial of $2N$ variables with equal pairs of indices.The mean values…
Particle distributions in squeezed states, even and odd coherent states are given in terms of multivariable Hermite polynomials. The Q--function and Wigner function for nonclassical field states are discussed.
Standard parton distribution function sets do not have rigorously quantified uncertainties. In recent years it has become apparent that these uncertainties play an important role in the interpretation of hadron collider data. In this paper,…
Complementarity relations between various characterizations of a probability distribution are at the core of information theory. In particular, lower and upper bounds for the entropic function are of great importance. In applied topics, we…
The uncertainty principle suggests a quantitative trade-off between the control of position and the control of momentum in particle propagation. However, a superposition of two states with very different uncertainty trade-offs introduces an…
The structure of the general solution of the inhomogeneous evolution equations allows the separation of a photon structure function into perturbative (``anomalous") and non-perturbative contributions. The former part is fully calculable,…
The idea to base the uncertainty relation for photons on the electromagnetic energy distribution in space enabled us to derive a sharp inequality that expresses the uncertainty relation [Phys. Rev. Lett. {\bf 108}, 140401 (2012)]. An…
Upper and lower bounds are obtained for the joint entropy of a collection of random variables in terms of an arbitrary collection of subset joint entropies. These inequalities generalize Shannon's chain rule for entropy as well as…
Rotated quadratures carry the phase-dependent information of the electromagnetic field, so they are somehow conjugate to the photon number. We analyze this noncanonical pair, finding an exact uncertatinty relation, as well as a couple of…
We discuss some inequalities for N nonnegative numbers. We use these inequalities to obtain known inequalities for probability distributions and new entropic and information inequalities for quantum tomograms of qudit states. The…
The even and odd coherent states are generalized for multimode case. The explicit forms for the photon distribution, Q-function and Wigner function are derived. In particular, it is shown that for two-mode case there exist strong…
Shannon information entropy is a natural measure of probability (de)localization and thus (un)predictability in various procedures of data analysis for model systems. We pay particular attention to links between the Shannon entropy and the…
Shannon entropy was defined for probability distributions and then its using was expanded to measure the uncertainty of knowledge for systems with complete information. In this article, it is proposed to extend the using of Shannon entropy…
We resort to the methods of statistical mechanics in order to determine the effects that a deformed dispersion relation has upon the thermodynamics of a photon gas. The ensuing modifications to the density of states, partition function,…
We present parton distribution functions which include a quantitative estimate of its uncertainties. The parton distribution functions are optimized with respect to deep inelastic proton data, expressing the uncertainties as a density…
The cumulants and factorial moments of photon distribution for squeezed and correlated light are calculated in terms of Chebyshev, Legendre and Laguerre polynomials. The phenomenon of strong oscillations of the ratio of the cumulant to…