scholarly journals On Some New Trapezoidal Type Inequalities for Twice (p,q) Differentiable Convex Functions in Post-Quantum Calculus

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1605
Author(s):  
Thanin Sitthiwirattham ◽  
Ghulam Murtaza ◽  
Muhammad Aamir Ali ◽  
Sotiris K. Ntouyas ◽  
Muhammad Adeel ◽  
...  
Keyword(s):  
Information Theory ◽  
Quantum Information ◽  
Computer Science ◽  
Convex Functions ◽  
Strong Association ◽  
Quantum Information Theory ◽  
Symmetric Convex ◽  
Quantum Calculus ◽  
Interdisciplinary Field ◽  
Science Information

Quantum information theory, an interdisciplinary field that includes computer science, information theory, philosophy, cryptography, and symmetry, has various applications for quantum calculus. Inequalities has a strong association with convex and symmetric convex functions. In this study, first we establish a p,q-integral identity involving the second p,q-derivative and then we used this result to prove some new trapezoidal type inequalities for twice p,q-differentiable convex functions. It is also shown that the newly established results are the refinements of some existing results in the field of integral inequalities. Analytic inequalities of this nature and especially the techniques involved have applications in various areas in which symmetry plays a prominent role.

scholarly journals Some Parameterized Quantum Midpoint and Quantum Trapezoid Type Inequalities for Convex Functions with Applications

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 996
Author(s):  
Suphawat Asawasamrit ◽  
Muhammad Aamir Ali ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Information Theory ◽  
Convex Functions ◽  
Strong Association ◽  
Type Inequality ◽  
Quadrature Formulas ◽  
Quantum Calculus ◽  
Interdisciplinary Field ◽  
Integral Equality ◽  
Entropy Functions ◽  
Science Information

Quantum information theory, an interdisciplinary field that includes computer science, information theory, philosophy, cryptography, and entropy, has various applications for quantum calculus. Inequalities and entropy functions have a strong association with convex functions. In this study, we prove quantum midpoint type inequalities, quantum trapezoidal type inequalities, and the quantum Simpson’s type inequality for differentiable convex functions using a new parameterized q-integral equality. The newly formed inequalities are also proven to be generalizations of previously existing inequities. Finally, using the newly established inequalities, we present some applications for quadrature formulas.

Quantum Information Science Vis-à-Vis Information Schools

2019 ◽  
pp. 199-211
Author(s):  
P. K. Paul ◽  
D. Chatterjee ◽  
A. Bhuimali
Keyword(s):  
Information Theory ◽  
Quantum Information ◽  
Computer Science ◽  
Quantum Physics ◽  
Information Science ◽  
New Paradigm ◽  
Quantum Information Science ◽  
Information Studies ◽  
Quantum Science ◽  
Science Information

Quantum information science (QIS) is a combination of quantum science (which combines radio physics, condensed physics, and electronics) and information science (which combines computer science, information technology, mathematics, information studies, and documentation studies). Quantum information science (QIS) is actually an extension of quantum computing. Quantum information science (QIS) is mistakenly taken as quantum information theory, but it has several differences with this. Quantum information science (QIS) is mainly responsible for improved and faster acquisition, transmission, and processing of information. The 20th century is marked by three monumental achievements, namely, computer science, quantum physics, and information theory, which have not only stunned the civilized world but also ushered into a new world – a new paradigm of science and technology.

scholarly journals Some applications of the Hermit-Hadamard inequality for log-convex functions in quantum divergence

2021 ◽  
Author(s):  
Fatemeh Hassanzad ◽  
Hossien Mehri-Dehnavi ◽  
Hamzeh Agahi
Keyword(s):  
Information Theory ◽  
Quantum Information ◽  
Relative Entropy ◽  
Convex Functions ◽  
Quantum Information Theory ◽  
Density Matrices ◽  
Hadamard Inequality ◽  
Quantum Relative Entropy ◽  
Nonlinear Anal ◽  
Jensen Shannon Divergence

One of the beautiful and very simple inequalities for a convex function is the Hermit-Hadamard inequality [S. Mehmood, et. al. Math. Methods Appl. Sci., 44 (2021) 3746], [S. Dragomir, et. al., Math. Methods Appl. Sci., in press]. The concept of log-convexity is a stronger property of convexity. Recently, the refined Hermit-Hadamard’s inequalities for log-convex functions were introduced by researchers [C. P. Niculescu, Nonlinear Anal. Theor., 75 (2012) 662]. In this paper, by the Hermit-Hadamard inequality, we introduce two parametric Tsallis quantum relative entropy, two parametric Tsallis-Lin quantum relative entropy and two parametric quantum Jensen-Shannon divergence in quantum information theory. Then some properties of quantum Tsallis-Jensen-Shannon divergence for two density matrices are investigated by this inequality. \newline \textbf{Keywords:} \textit{ Hermit-Hadamard’s inequality; log-convexity; Density matrices; Quantum relative entropy; Tsallis quantum relative entropy; quantum Jensen-Shannon divergence divergence.

QALO-MOR: Improved antlion optimizer based on quantum information theory for model order reduction

2021 ◽  
pp. 1-11
Author(s):  
Rosy Pradhan ◽  
Mohammad Rafique Khan ◽  
Prabir Kumar Sethy ◽  
Santosh Kumar Majhi
Keyword(s):  
Information Theory ◽  
Quantum Information ◽  
Real World ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Quantum Information Theory ◽  
Hunting Behavior ◽  
Model Order ◽  
Ant Lion Optimization ◽  
Real World Problems

The field of optimization science is proliferating that has made complex real-world problems easy to solve. Metaheuristics based algorithms inspired by nature or physical phenomena based methods have made its way in providing near-ideal (optimal) solutions to several complex real-world problems. Ant lion Optimization (ALO) has inspired by the hunting behavior of antlions for searching for food. Even with a unique idea, it has some limitations like a slower rate of convergence and sometimes confines itself into local solutions (optima). Therefore, to enhance its performance of classical ALO, quantum information theory is hybridized with classical ALO and named as QALO or quantum theory based ALO. It can escape from the limitations of basic ALO and also produces stability between processes of explorations followed by exploitation. CEC2017 benchmark set is adopted to estimate the performance of QALO compared with state-of-the-art algorithms. Experimental and statistical results demonstrate that the proposed method is superior to the original ALO. The proposed QALO extends further to solve the model order reduction (MOR) problem. The QALO based MOR method performs preferably better than other compared techniques. The results from the simulation study illustrate that the proposed method effectively utilized for global optimization and model order reduction.

scholarly journals Entanglement and Disordered-Enhanced Topological Phase in the Kitaev Chain

Universe ◽  
2019 ◽  
Vol 5 (1) ◽  
pp. 33 ◽  
Author(s):  
Liron Levy ◽  
Moshe Goldstein
Keyword(s):  
Phase Diagram ◽  
Information Theory ◽  
Quantum Information ◽  
Critical Point ◽  
Entanglement Entropy ◽  
Quantum Information Theory ◽  
Topological Phase ◽  
Many Body ◽  
Zero Modes ◽  
Many Body Systems

In recent years, tools from quantum information theory have become indispensable in characterizing many-body systems. In this work, we employ measures of entanglement to study the interplay between disorder and the topological phase in 1D systems of the Kitaev type, which can host Majorana end modes at their edges. We find that the entanglement entropy may actually increase as a result of disorder, and identify the origin of this behavior in the appearance of an infinite-disorder critical point. We also employ the entanglement spectrum to accurately determine the phase diagram of the system, and find that disorder may enhance the topological phase, and lead to the appearance of Majorana zero modes in systems whose clean version is trivial.

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