scholarly journals Influence of Noise Channel in Quantum One Time Password Authentication

2020 ◽  
Author(s):  
Mohit Kr sharma ◽  
Manisha J. Nena
Keyword(s):  
Communication Theory ◽  
Quantum Noise ◽  
User Authentication ◽  
Quantum Information Theory ◽  
Mathematical Tool ◽  
One Time Password ◽  
Noise Models ◽  
Influence Of Noise ◽  
Kraus Operators ◽  
Powerful Mathematical Tool

This paper presents an overview of quantum errors and noise channels, their mathematical modeling and its implementation in quantum one time password (QOTP) based user authentication. Quantum noise plays a pivotal role in understanding quantum information theory which is important to build up quantum communication theory. The Kraus operators provide a powerful mathematical tool in understanding and modeling various quantum channels. Use of QOTP provides an impressive method of carrying out user authentication involving quantum operations based on user biometrics. However, the efficiency of this method can be better envisaged by incorporating noise models during qubit transmission.

scholarly journals Application of He’s Variational Iteration Method to Nonlinear Integro-Differential Equations

2010 ◽  
Vol 65 (5) ◽  
pp. 418-430 ◽  
Author(s):  
Ahmet Yildirim
Keyword(s):  
Differential Equations ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Mathematical Tool ◽  
Variational Iteration ◽  
He’S Variational Iteration Method ◽  
Powerful Mathematical Tool

In this paper, an application of He’s variational iteration method is applied to solve nonlinear integro-differential equations. Some examples are given to illustrate the effectiveness of the method. The results show that the method provides a straightforward and powerful mathematical tool for solving various nonlinear integro-differential equations

Determination of the Limit Cycle by He’s Parameter-Expansion for Oscillators in a u3 / (1 + u2) Potential

2007 ◽  
Vol 62 (7-8) ◽  
pp. 396-398 ◽  
Author(s):  
Li-Na Zhang ◽  
Lan Xu
Keyword(s):  
Exact Solutions ◽  
Limit Cycle ◽  
Limit Cycles ◽  
Expansion Method ◽  
Nonlinear Oscillators ◽  
Mathematical Tool ◽  
Parameter Expansion ◽  
Parameter Expansion Method ◽  
Powerful Mathematical Tool

This paper applies He’s parameter-expansion method to determine the limit cycle of oscillators in a u3/(1+u2) potential. The results are compared with the exact solutions. This shows that the method is a convenient and powerful mathematical tool for the search of limit cycles of nonlinear oscillators.

scholarly journals Application of He's Variational Iteration Method to Solve Semidifferential Equations of th Order

2008 ◽  
Vol 2008 ◽  
pp. 1-9 ◽  
Author(s):  
Asghar Ghorbani ◽  
Abdolsaeed Alavi
Keyword(s):  
Iteration Method ◽  
Present Method ◽  
Variational Iteration Method ◽  
Convergent Series ◽  
Mathematical Tool ◽  
Spline Method ◽  
Weak Nonlinearity ◽  
Variational Iteration ◽  
He’S Variational Iteration Method ◽  
Powerful Mathematical Tool

He's variational iteration method is applied to solve th order semidifferential equations. Comparison is made between collocation spline method based on Lagrange interpolation and the present method. In this method, the solution is calculated in the form of a convergent series with an easily computable component. This approach does not need linearization, weak nonlinearity assumptions, or perturbation theory. Some examples are given to illustrate the effectiveness of the method; the results show that He's method provides a straightforward and powerful mathematical tool for solving various semidifferential equations of the th order.

On soft ordered ternary semihypergroups

2018 ◽  
Vol 7 (1-2) ◽  
pp. 27-39
Author(s):  
Muhammad Farooq ◽  
Asghar Khan ◽  
Muhammad Izhar ◽  
Bijan Davvaz
Keyword(s):  
General Framework ◽  
Mathematical Tool ◽  
Soft Sets ◽  
Powerful Mathematical Tool

Theory of soft sets proposed by Molodtsov as a general framework for reasoning about vague concepts is a powerful mathematical tool for modelling various types of uncertainties. In this paper, we introduce the notions of intersectional soft subsemihypergroup, intersectional soft left (lateral, right) hyperideal of ordered ternary semihypergroups and related properties are investigated. We present characterizations of right weakly regular ordered ternary semihypergroups by means of intersectional hyperideals.

scholarly journals Exact Explicit Traveling Wave Solution for the Generalized (2+1)-Dimensional Boussinesq Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-10
Author(s):  
Libing Zeng ◽  
Keding Qin ◽  
Shengqiang Tang
Keyword(s):  
Traveling Wave ◽  
Boussinesq Equation ◽  
Nonlinear Partial Differential Equations ◽  
Mathematical Physics ◽  
Traveling Wave Solution ◽  
Mathematical Tool ◽  
Extended Tanh Method ◽  
Physical Problems ◽  
Tanh Method ◽  
Powerful Mathematical Tool

The sine-cosine method and the extended tanh method are used to construct exact solitary patterns solution and compactons solutions of the generalized (2+1)-dimensional Boussinesq equation. The compactons solutions and solitary patterns solutions of the generalized (2+1)-dimensional Boussinesq equation are successfully obtained. These solutions may be important and of significance for the explanation of some practical physical problems. It is shown that the sine-cosine and the extended tanh methods provide a powerful mathematical tool for solving great many nonlinear partial differential equations in mathematical physics.

scholarly journals Symmetry reduction a promising method for heat conduction equations

2019 ◽  
Vol 23 (4) ◽  
pp. 2219-2227
Author(s):  
Yi Tian
Keyword(s):  
Heat Conduction ◽  
Exact Solutions ◽  
Wave Equations ◽  
Reduction Method ◽  
Variational Iteration Method ◽  
Mathematical Tool ◽  
Approximate Methods ◽  
Similarity Reduction ◽  
Homotopy Perturbation ◽  
Powerful Mathematical Tool

Though there are many approximate methods, e. g., the variational iteration method and the homotopy perturbation, for non-linear heat conduction equations, exact solutions are needed in optimizing the heat problems. Here we show that the Lie symmetry and the similarity reduction provide a powerful mathematical tool to searching for the needed exact solutions. Lie algorithm is used to obtain the symmetry of the heat conduction equations and wave equations, then the studied equations are reduced by the similarity reduction method.

scholarly journals Pauli error estimation via Population Recovery

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 549
Author(s):  
Steven T. Flammia ◽  
Ryan O'Donnell
Keyword(s):  
Error Estimation ◽  
Quantum Noise ◽  
Measurement Data ◽  
Simple Algorithm ◽  
Error Rates ◽  
Measurement Noise ◽  
Population Recovery ◽  
State Preparation ◽  
Noise Models ◽  
Recovery Problem

Motivated by estimation of quantum noise models, we study the problem of learning a Pauli channel, or more generally the Pauli error rates of an arbitrary channel. By employing a novel reduction to the "Population Recovery" problem, we give an extremely simple algorithm that learns the Pauli error rates of an n-qubit channel to precision ϵ in ℓ∞ using just O(1/ϵ2)log⁡(n/ϵ) applications of the channel. This is optimal up to the logarithmic factors. Our algorithm uses only unentangled state preparation and measurements, and the post-measurement classical runtime is just an O(1/ϵ) factor larger than the measurement data size. It is also impervious to a limited model of measurement noise where heralded measurement failures occur independently with probability ≤1/4.We then consider the case where the noise channel is close to the identity, meaning that the no-error outcome occurs with probability 1−η. In the regime of small η we extend our algorithm to achieve multiplicative precision 1±ϵ (i.e., additive precision ϵη) using just O(1ϵ2η)log⁡(n/ϵ) applications of the channel.

scholarly journals Tutorial on EM Algorithm

2018 ◽  
Author(s):  
Loc Nguyen
Keyword(s):  
Em Algorithm ◽  
Likelihood Function ◽  
Joint Probability ◽  
Likelihood Estimation ◽  
Mathematical Tool ◽  
Probability And Statistics ◽  
Hidden Data ◽  
Parameter Estimators ◽  
The Relationship ◽  
Powerful Mathematical Tool

Maximum likelihood estimation (MLE) is a popular method for parameter estimation in both applied probability and statistics but MLE cannot solve the problem of incomplete data or hidden data because it is impossible to maximize likelihood function from hidden data. Expectation maximum (EM) algorithm is a powerful mathematical tool for solving this problem if there is a relationship between hidden data and observed data. Such hinting relationship is specified by a mapping from hidden data to observed data or by a joint probability between hidden data and observed data. In other words, the relationship helps us know hidden data by surveying observed data. The essential ideology of EM is to maximize the expectation of likelihood function over observed data based on the hinting relationship instead of maximizing directly the likelihood function of hidden data. Pioneers in EM algorithm proved its convergence. As a result, EM algorithm produces parameter estimators as well as MLE does. This tutorial aims to provide explanations of EM algorithm in order to help researchers comprehend it.

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