Analysis of Negativity and Relative Entropy of Entanglement Measures for Two Qutrit Quantum Communication Systems

Erol, Volkan

doi:10.20944/preprints201703.0217.v1

Cited by 11 publications

(9 citation statements)

References 36 publications

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“…Many recent researches have been done in entanglement and its related disciplines like entanglement measures and majorization, etc. [12][13][14][15][16][17][18][19][20]. One of the main applications of quantum computing is solving optimization problems.…”

Section: Introductionmentioning

confidence: 99%

Applying Quantum Optimization Algorithms for Linear Programming

Side¹,

Erol²

2017

Preprint

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Quantum computers are machines that are designed to use quantum mechanics in order to improve upon classical computers by running quantum algorithms. One of the main applications of quantum computing is solving optimization problems. For addressing optimization problems we can use linear programming. Linear programming is a method to obtain the best possible outcome in a special case of mathematical programming. Application areas of this problem consist of resource allocation, production scheduling, parameter estimation, etc. In our study, we looked at the duality of resource allocation problems. First, we chose a real world optimization problem and looked at its solution with linear programming. Then, we restudied this problem with a quantum algorithm in order to understand whether if there is a speedup of the solution. The improvement in computation is analysed and some interesting results are reported.

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Section: Introductionmentioning

confidence: 99%

Applying Quantum Optimization Algorithms for Linear Programming

Side¹,

Erol²

2017

Preprint

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Section: Introductionmentioning

confidence: 99%

Detecting Quantum Speedup of HHL Algorithm for Linear Programming Scenarios

Erol¹,

Side²

2017

Preprint

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Quantum computers are machines that are designed to use quantum mechanics in order to improve upon classical computers by running quantum algorithms. One of the main applications of quantum computing is solving optimization problems. For addressing optimization problems, we can use linear programming. Linear programming is a method to obtain the best possible outcome in a special case of mathematical programming. Application areas of this problem consist of resource allocation, production scheduling, parameter estimation, etc. In our study, we look at quantum speedup ratios of HHL Algorithm for different scenarios of linear programming. In a first scenario we look quantum speedup ratio (S(N)) as a function of phase transition and the ratio (κ) between the greatest and smallest eigenvalues of the matrix in linear equation system. As a second scenario, we investigate the changes in S(N) as a function of κ and s, which is the coefficient for defining the matrix as s-sparse.

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“…Many recent research has been done in entanglement and its related disciplines like entanglement measures and majorization, etc. [12][13][14][15][16][17][18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Behaviour of Quantum Correlations and Violation of Bell Inequalities in some Noisy Channels

Erol¹

2017

Preprint

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Quantum Correlations are studied extensively in quantum information domain. Entanglement Measures and Quantum Discord are good examples of these actively studied correlations. Detection of violation in Bell inequalities is also a widely active area in quantum information theory world. In this work, we revisit the problem of analyzing the behavior of quantum correlations and violation of Bell inequalities in noisy channels. We extend the problem defined in a recent study by observing the changes in negativity measure, quantum discord and a modified version of Horodecki measure for violation of Bell inequalities under amplitude damping, phase damping and depolarizing channels. We report different interesting results for each of these correlations and measures. All these correlations and measures decrease under decoherence channels, but some changes are very dramatical comparing to others. We investigate also separability conditions of example studied states.

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Analysis of Negativity and Relative Entropy of Entanglement Measures for Two Qutrit Quantum Communication Systems

Cited by 11 publications

References 36 publications

Applying Quantum Optimization Algorithms for Linear Programming

Applying Quantum Optimization Algorithms for Linear Programming

Detecting Quantum Speedup of HHL Algorithm for Linear Programming Scenarios

Behaviour of Quantum Correlations and Violation of Bell Inequalities in some Noisy Channels

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