scholarly journals On the Mathematical Boundaries of Communication with Zero-Capacity Quantum Channels

10.29007/7h1q ◽  
2018 ◽  
Author(s):  
Laszlo Gyongyosi ◽  
Sandor Imre
Keyword(s):  
Information Theory ◽  
Quantum Information ◽  
21St Century ◽  
Quantum Information Theory ◽  
Quantum Mechanical ◽  
Quantum Channels ◽  
Classical Systems ◽  
Quantum Relative Entropy ◽  
Mathematical Properties ◽  
Zero Capacity

In the first decade of the 21st century, many revolutionary properties of quantum channels were discovered. These phenomena are purely quantum mechanical and completely unimaginable in classical systems. Recently, the most important discovery in Quantum Information Theory was the possibility of transmitting quantum information over zero-capacity quantum channels. In this work we prove that the possibility of superactivation of quantum channel capacities is determined by the mathematical properties of the quantum relative entropy function.

AN OPERATIONAL ALGEBRAIC APPROACH TO QUANTUM CHANNEL CAPACITY

2008 ◽  
Vol 06 (05) ◽  
pp. 981-996 ◽  
Author(s):  
V. P. BELAVKIN ◽  
X. DAI
Keyword(s):  
Information Theory ◽  
Quantum Information ◽  
Quantum Channel ◽  
Algebraic Approach ◽  
Quantum Information Theory ◽  
Quantum Channels ◽  
Operational Approach ◽  
Quantum Relative Entropy ◽  
Quantum Mutual Information ◽  
Arbitrary Quantum

An elementary introduction into algebraic approach to unified quantum information theory and operational approach to quantum entanglement as generalized encoding is given. After introducing compound quantum state and two types of informational divergences, namely, Araki–Umegaki (a-type) and of Belavkin–Staszewski (b-type) quantum relative entropic information, this paper treats two types of quantum mutual information via entanglement and defines two types of corresponding quantum channel capacities as the supremum via the generalized encodings. It proves the additivity property of quantum channel capacities via entanglement, which extends the earlier results of Belavkin to products of arbitrary quantum channels for quantum relative entropy of any type.

QUANTUM ENTROPIES AND ENTANGLEMENT

2005 ◽  
Vol 03 (01) ◽  
pp. 99-104 ◽  
Author(s):  
J. BATLE ◽  
M. CASAS ◽  
A. R. PLASTINO ◽  
A. PLASTINO
Keyword(s):  
Information Theory ◽  
Quantum Information ◽  
Relative Entropy ◽  
Conditional Entropy ◽  
Quantum Information Theory ◽  
Total Entropy ◽  
Separability Criterion ◽  
Quantum Relative Entropy ◽  
Entanglement Of Formation

The nature of quantum entropies, and its use in Quantum Information Theory in the form of (i) total entropy, (ii) relative entropy and (iii) conditional entropy is revisited. In this ordering, we first show the correlations existing between the total q-entropy and entanglement, quantified in the form of entanglement of formation. Then, we revisit the use of the quantum relative entropy as a measure of entanglement, and we finally discuss some features of the quantum conditional q-entropies, which are used in turn as a separability criterion.

scholarly journals SINGULAR VALUE DECOMPOSITION AND MATRIX REORDERINGS IN QUANTUM INFORMATION THEORY

2011 ◽  
Vol 22 (09) ◽  
pp. 897-918 ◽  
Author(s):  
JAROSŁAW ADAM MISZCZAK
Keyword(s):  
Information Theory ◽  
Quantum Information ◽  
Singular Value Decomposition ◽  
Computing System ◽  
Quantum Information Theory ◽  
Singular Value ◽  
Quantum States ◽  
Quantum Channels ◽  
Basic Functions ◽  
Value Decomposition

We review Schmidt and Kraus decompositions in the form of singular value decomposition using operations of reshaping, vectorization and reshuffling. We use the introduced notation to analyze the correspondence between quantum states and operations with the help of Jamiołkowski isomorphism. The presented matrix reorderings allow us to obtain simple formulae for the composition of quantum channels and partial operations used in quantum information theory. To provide examples of the discussed operations, we utilize a package for the Mathematica computing system implementing basic functions used in the calculations related to quantum information theory.

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.

scholarly journals Recoverability in quantum information theory

2015 ◽  
Vol 471 (2182) ◽  
pp. 20150338 ◽  
Author(s):  
Mark M. Wilde
Keyword(s):  
Information Theory ◽  
Quantum Information ◽  
Relative Entropy ◽  
Entropy Inequality ◽  
Quantum Information Theory ◽  
The Other ◽  
Complex Interpolation ◽  
The Core ◽  
Quantum Relative Entropy ◽  
Entropy Inequalities

The fact that the quantum relative entropy is non-increasing with respect to quantum physical evolutions lies at the core of many optimality theorems in quantum information theory and has applications in other areas of physics. In this work, we establish improvements of this entropy inequality in the form of physically meaningful remainder terms. One of the main results can be summarized informally as follows: if the decrease in quantum relative entropy between two quantum states after a quantum physical evolution is relatively small, then it is possible to perform a recovery operation, such that one can perfectly recover one state while approximately recovering the other. This can be interpreted as quantifying how well one can reverse a quantum physical evolution. Our proof method is elementary, relying on the method of complex interpolation, basic linear algebra and the recently introduced Rényi generalization of a relative entropy difference. The theorem has a number of applications in quantum information theory, which have to do with providing physically meaningful improvements to many known entropy inequalities.

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.

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