Related papers: A Generalized Euler Probability Distribution
We revisit the Perelomov SU(1,1) displaced coherent states states as possible quantum states of light. We disclose interesting statistical aspects of these states in relation with photon counting and squeezing. In the non-displaced case we…
In this review article we present different formal frameworks for the description of generalized probabilities in statistical theories. We discuss the particular cases of probabilities appearing in classical and quantum mechanics, possible…
A distribution of electromagnetic fields presents a statistical assembly of a particular type, which is at scale h a quantum statistical assembly itself and has also been instrumental to concretisation of the basic probability assumption of…
The framework of generalized probabilistic theories is a powerful tool for studying the foundations of quantum physics. It provides the basis for a variety of recent findings that significantly improve our understanding of the rich physical…
Random variables of the generalized Pareto distribution, can be transformed to that of the Pareto distribution. Explicit expressions exist for the maximum likelihood estimators of the parameters of the Pareto distribution. The performance…
We investigate a generalized empirical likelihood approach in a two-group setting where the constraints on parameters have a form of U-statistics. In this situation, the summands that consist of the constraints for the empirical likelihood…
First-order statistics of scattered light is described using the representation of probability density cloud which visualizes a two-dimensional distribution for complex amplitude. The geometric parameters of the cloud are studied in detail…
By introducing the thermo entangled state representation, we derived four new photocount distribution formulas for a given density operator of light field. It is shown that these new formulas, which is convenient to calculate the…
After studying some properties of the generalized exponential and logarithmic function, in particular investigating the domain where the first maintains itself real and positive, and outlining how the known dualities $q \leftrightarrow…
Physics is based on probabilities as fundamental entities of a mathematical description. Expectation values of observables are computed according to the classical statistical rule. The overall probability distribution for one world covers…
Generalized linear statistics are an unifying class that contains U-statistics, U-quantiles, L-statistics as well as trimmed and winsorized U-statistics. For example, many commonly used estimators of scale fall into this class.…
In this paper, we will present a general formalism for constructing the nonlinear charge coherent states which in special case lead to the standard charge coher- ent states. The suQ(1;1) algebra as a nonlinear deformed algebra realization…
We present the full characterization of phase-randomized or phase-averaged coherent states, a class of states exploited in communication channels and in decoy state-based quantum key distribution protocols. In particular, we report on the…
We introduce a family of coefficients based on U-statistics that generalize the notion of correlation and explore their properties in the large dimensional multivariate case, showing that in the null case of uncorrelated variables, the…
A geometric framework for quantum statistical estimation is used to establish a series of higher order corrections to the Heisenberg uncertainty relations associated with pairs of canonically conjugate variables. These corrections can be…
A $q$-deformed Weyl-Heisenberg algebra is used to define a deformed displacement operator giving rise to a naturally normalized nonlinear coherent states type. Robust maximally entangled deformed coherent states are studied and the effect…
In this paper we introduce the generalization of Multi Poly-Euler polynomials and we investigate some relationship involving Multi Poly-Euler polynomials. Obtaining a closed formula for generalization of Multi Poly-Euler numbers therefore…
This survey gives a comprehensive account of quantum correlations understood as a phenomenon stemming from the rules of quantization. Centered on quantum probability it describes the physical concepts related to correlations (both classical…
The notion of standard positive probability distribution function (tomogram) which describes the quantum state of universe alternatively to wave function or to density matrix is introduced. Connection of the tomographic probability…
The purpose of this paper is to introduce several basic theorems of coherent states and generalized coherent states based on Lie algebras su(2) and su(1,1), and to give some applications of them to quantum information theory for graduate…