scholarly journals Maximally Entangled SU(1,1) Semi Coherent States

2021 ◽  
Author(s):  
A.-S. F. Obada ◽  
M. M. A. Ahmed ◽  
Hoda A. Ali ◽  
Somia Abd-Elnabi ◽  
S. Sanad
Keyword(s):  
Distribution Function ◽  
Correlation Function ◽  
Probability Distribution Function ◽  
Coherent States ◽  
Distribution Functions ◽  
Entangled States ◽  
Nonclassical Properties ◽  
Quadrature Squeezing ◽  
Maximally Entangled States ◽  
Quasiprobability Distribution

AbstractIn this paper, we consider a special type of maximally entangled states namely by entangled SU(1,1) semi coherent states by using SU(1,1) semi coherent states(SU(1,1) Semi CS). The entanglement characteristics of these entangled states are studied by evaluating the concurrence.We investigate some of their nonclassical properties,especially probability distribution function,second-order correlation function and quadrature squeezing . Further, the quasiprobability distribution functions (Q-functions) is discussed.

INFLUENCE OF SQUEEZING OPERATOR ON THE QUANTUM PROPERTIES OF VARIOUS BINOMIAL STATES

2001 ◽  
Vol 15 (01) ◽  
pp. 75-100 ◽  
Author(s):  
FAISAL A. A. EL-ORANY ◽  
M. SEBAWE ABDALLA ◽  
A-.S. F. OBADA ◽  
G. M. ABD AL-KADER
Keyword(s):  
Distribution Function ◽  
Correlation Function ◽  
Phase Distribution ◽  
Single Mode ◽  
Second Order ◽  
Distribution Functions ◽  
Quantum Properties ◽  
Quadrature Phase ◽  
Squeezing Operator ◽  
Quasiprobability Distribution

In this communication we investigate the action of a single-mode squeeze operator on the statistical behaviour of different binomial states. For the resulting states (squeezed generalized binomial states) normalized second-order correlation function, quasiprobability distribution functions and the distribution function P(x) associated with the quadrature x are studied both analytically and numerically. Furthermore, the quadrature phase distribution as well as the phase distribution in the framework of Pegg–Barnett formalism are discussed.

The Method of Probabilistic Nodes Combination in Decision Making and Risk Analysis

2016 ◽  
pp. 32-60
Author(s):  
Dariusz Jacek Jakóbczak
Keyword(s):  
Decision Making ◽  
Distribution Function ◽  
Probability Distribution ◽  
Risk Analysis ◽  
Probability Distribution Function ◽  
Linear Interpolation ◽  
Distribution Functions ◽  
Probability Distribution Functions ◽  
Characteristic Points ◽  
Basic Probability

Proposed method, called Probabilistic Nodes Combination (PNC), is the method of 2D curve interpolation and extrapolation using the set of key points (knots or nodes). Nodes can be treated as characteristic points of data for modeling and analyzing. The model of data can be built by choice of probability distribution function and nodes combination. PNC modeling via nodes combination and parameter ? as probability distribution function enables value anticipation in risk analysis and decision making. Two-dimensional curve is extrapolated and interpolated via nodes combination and different functions as discrete or continuous probability distribution functions: polynomial, sine, cosine, tangent, cotangent, logarithm, exponent, arc sin, arc cos, arc tan, arc cot or power function. Novelty of the paper consists of two generalizations: generalization of previous MHR method with various nodes combinations and generalization of linear interpolation with different (no basic) probability distribution functions and nodes combinations.

scholarly journals The Fréchet transform

1993 ◽  
Vol 16 (1) ◽  
pp. 155-164
Author(s):  
Piotor Mikusiński ◽  
Morgan Phillips ◽  
Howard Sherwood ◽  
Michael D. Taylor
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Probability Measure ◽  
Probability Distribution Function ◽  
Random Variables ◽  
Distribution Functions ◽  
Probability Distribution Functions

LetF1,…,FNbe1-dimensional probability distribution functions andCbe anN-copula. Define anN-dimensional probability distribution functionGbyG(x1,…,xN)=C(F1(x1),…,FN(xN)). Letν, be the probability measure induced onℝNbyGandμbe the probability measure induced on[0,1]NbyC. We construct a certain transformationΦof subsets ofℝNto subsets of[0,1]Nwhich we call the Fréchet transform and prove that it is measure-preserving. It is intended that this transform be used as a tool to study the types of dependence which can exist between pairs orN-tuples of random variables, but no applications are presented in this paper.

Decision Making and Data Analysis

2021 ◽  
pp. 52-81
Author(s):  
Dariusz Jacek Jakóbczak
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Probability Distribution Function ◽  
Distribution Functions ◽  
Two Dimensional ◽  
Key Points ◽  
Characteristic Points ◽  
Writer Recognition ◽  
Curve Modeling ◽  
Specific Letter

The proposed method, called probabilistic nodes combination (PNC), is the method of 2D curve modeling and handwriting identification by using the set of key points. Nodes are treated as characteristic points of signature or handwriting for modeling and writer recognition. Identification of handwritten letters or symbols need modeling, and the model of each individual symbol or character is built by a choice of probability distribution function and nodes combination. PNC modeling via nodes combination and parameter γ as probability distribution function enables curve parameterization and interpolation for each specific letter or symbol. Two-dimensional curve is modeled and interpolated via nodes combination and different functions as continuous probability distribution functions: polynomial, sine, cosine, tangent, cotangent, logarithm, exponent, arc sin, arc cos, arc tan, arc cot, or power function.

SUPERPOSITIONS OF SQUEEZED COHERENT STATES: PROPERTIES AND GENERATION

1999 ◽  
Vol 13 (17) ◽  
pp. 2299-2312 ◽  
Author(s):  
A.-S. F. OBADA ◽  
G. M. ABD AL-KADER
Keyword(s):  
Distribution Function ◽  
Phase Space ◽  
Coherent States ◽  
Phase Distribution ◽  
Coherence Function ◽  
Photon Number ◽  
Distribution Functions ◽  
Numerical Results ◽  
Quadrature Component ◽  
Photon Number Distribution

The s-parameterized charactristic function for the superposition of squeezed coherent states (SCS's) is given. The s-parameterized distribution functions for the superposition of SCS's are investigated. Various moments are calculated by using this charactristic function. The Glauber second-order coherence function is calculated. The photon number distribution of the superposition of SCS's studied. Analytical and numerical results for the quadrature component distributions for the superposition of a pair of SCS's are presented. The phase distribution calculated from the integration of s-parameterized distribution function over the phase space. A generation scheme is discussed.

Photon-catalyzed optical coherent states generated via a non-degenerate parametric amplifier with quantum-optical catalysis

2020 ◽  
Vol 98 (2) ◽  
pp. 119-124 ◽  
Author(s):  
Hong-Chun Yuan ◽  
Xue-Xiang Xu ◽  
Heng-Mei Li ◽  
Ye-Jun Xu ◽  
Xiang-Guo Meng
Keyword(s):  
Coherent State ◽  
Wigner Function ◽  
Coherent States ◽  
Laguerre Polynomial ◽  
Photon Number ◽  
Parametric Amplifier ◽  
Normalization Factor ◽  
Nonclassical Properties ◽  
Quadrature Squeezing ◽  
Quantum Optical

We theoretically generate a kind of photon-catalyzed optical coherent states (PCOCSs) by heralded interference between any photons and coherent state via a non-degenerate parametric amplifier, which is also just a Laguerre polynomial excited coherent state. Based on obtaining the probability of successfully detecting them (also the normalization factor), the nonclassical properties of the PCOCSs are analytically investigated according to autocorrelation function, quadrature squeezing, and the negativity of the Wigner function. It is found that the nonclassicality depends on the amplitude of the coherent state, the catalysis photon number, and amplifier parameter. The negative volume of their Wigner function can be enlarged by increasing the catalysis photon number. These parameters may be effectively used to improve and enhance the nonclassical characteristics.

GENERALIZED EXCITED NEGATIVE BINOMIAL STATES OF ELECTROMAGNETIC FIELD AND SOME OF THEIR NON-CLASSICAL PROPERTIES

2003 ◽  
Vol 17 (07) ◽  
pp. 1071-1086 ◽  
Author(s):  
H. H. SALAH ◽  
M. DARWISH ◽  
A.-S. F. OBADA
Keyword(s):  
Electromagnetic Field ◽  
Correlation Function ◽  
Probability Distribution ◽  
Wigner Function ◽  
Coherent States ◽  
Negative Binomial ◽  
Distribution Functions ◽  
Probability Distribution Functions ◽  
New States ◽  
Q Function

New states of electromagnetic field, generalized excited negative binomial states are introduced here. These states interpolate between the superposition of two excited coherent states and number states. The non-classical properties for these states are discussed, such as, second order correlation function, squeezing phenomena [normal squeezing and amplitude squared squeezing], phase properties in Pegg–Barnett formalism and the quasi-probability distribution functions (Q-function and Wigner function).

scholarly journals Optimal Sampling of Parametric Families: Implications for Machine Learning

2020 ◽  
Vol 32 (1) ◽  
pp. 261-279
Author(s):  
Adrian E. G. Huber ◽  
Jithendar Anumula ◽  
Shih-Chii Liu
Keyword(s):  
Machine Learning ◽  
Distribution Function ◽  
Probability Distribution ◽  
Probability Distribution Function ◽  
Distribution Functions ◽  
Test Set ◽  
Probability Distribution Functions ◽  
Parametric Families ◽  
The Continuum ◽  
Training Sets

It is well known in machine learning that models trained on a training set generated by a probability distribution function perform far worse on test sets generated by a different probability distribution function. In the limit, it is feasible that a continuum of probability distribution functions might have generated the observed test set data; a desirable property of a learned model in that case is its ability to describe most of the probability distribution functions from the continuum equally well. This requirement naturally leads to sampling methods from the continuum of probability distribution functions that lead to the construction of optimal training sets. We study the sequential prediction of Ornstein-Uhlenbeck processes that form a parametric family. We find empirically that a simple deep network trained on optimally constructed training sets using the methods described in this letter can be robust to changes in the test set distribution.

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