scholarly journals Constrained dynamics of maximally entangled bipartite system

2021 ◽  
Vol 81 (4) ◽  
Author(s):  
Asma Bashir ◽  
Muhammad Abdul Wasay
Keyword(s):  
External Field ◽  
Upper Bound ◽  
Quantum Dynamics ◽  
Direct Relationship ◽  
Composite System ◽  
No Reduction ◽  
Bipartite Entanglement ◽  
Constrained Dynamics ◽  
Bipartite System ◽  
Quantum Hamiltonian

AbstractThe classical and quantum dynamics of two particles constrained on $$S^1$$ S 1 is discussed via Dirac’s approach. We show that when state is maximally entangled between two subsystems, the product of dispersion in the measurement reduces. We also quantify the upper bound on the external field $$\vec {B}$$ B → such that $$\vec {B}\ge \vec {B}_{upper }$$ B → ≥ B → upper implies no reduction in the product of dispersion pertaining to one subsystem. Further, we report on the cut-off value of the external field $$\vec {B}_{cutoff }$$ B → cutoff , above which the bipartite entanglement is lost and there exists a direct relationship between uncertainty of the composite system and the external field. We note that, in this framework it is possible to tune the external field for entanglement/unentanglement of a bipartite system. Finally, we show that the additional terms arising in the quantum Hamiltonian, due to the requirement of Hermiticity of operators, produce a shift in the energy of the system.

On measures of quantum entanglement — A brief review

2016 ◽  
Vol 14 (06) ◽  
pp. 1640024 ◽  
Author(s):  
Debasis Sarkar
Keyword(s):  
Quantum Mechanics ◽  
Information Processing ◽  
Quantum Information ◽  
Quantum Entanglement ◽  
Quantum Correlation ◽  
Composite System ◽  
Quantum Information Processing ◽  
Bipartite Entanglement

Entanglement is one of the most useful resources in quantum information processing. It is effectively the quantum correlation between different subsystems of a composite system. Mathematically, one of the most hard tasks in quantum mechanics is to quantify entanglement. However, progress in this field is remarkable but not complete yet. There are many things to do with quantification of entanglement. In this review, we will discuss some of the important measures of bipartite entanglement.

scholarly journals A generalized fidelity amplitude for open systems

2016 ◽  
Vol 374 (2069) ◽  
pp. 20150162 ◽  
Author(s):  
T. Gorin ◽  
H. J. Moreno ◽  
T. H. Seligman
Keyword(s):  
Open System ◽  
Quantum Dynamics ◽  
Chaotic Dynamics ◽  
Composite System ◽  
Open Systems ◽  
Markov Approximation ◽  
Central System ◽  
Stabilizing Effect ◽  
Analytical Result ◽  
Intermediate System

We consider a central system which is coupled via dephasing to an open system, i.e. an intermediate system which in turn is coupled to another environment. Considering the intermediate and far environment as one composite system, the coherences in the central system are given in the form of fidelity amplitudes for a certain perturbed echo dynamics in the composite environment. On the basis of the Born–Markov approximation, we derive a master equation for the reduction of that dynamics to the intermediate system alone. In distinction to an earlier paper (Moreno et al . 2015 Phys. Rev. A 92, 030104. ( doi:10.1103/PhysRevA.92.030104 )), where we discussed the stabilizing effect of the far environment on the decoherence in the central system, we focus here on the possibility of using the measurable coherences in the central system for probing the open quantum dynamics in the intermediate system. We illustrate our results for the case of chaotic dynamics in the near environment, where we compare random matrix simulations with our analytical result.

scholarly journals Entanglement revive and information flow within the decoherent environment

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Jia-dong Shi ◽  
Dong Wang ◽  
Liu Ye
Keyword(s):  
Information Flow ◽  
Composite System ◽  
Theoretic Approach ◽  
Noisy Environment ◽  
Bipartite Entanglement ◽  
State Information ◽  
Information Theoretic ◽  
Correlation Distribution ◽  
Information Theoretic Approach ◽  
Insight Into

Abstract In this paper, the dynamics of entanglement is investigated in the presence of a noisy environment. We reveal its revival behavior and probe the mechanisms of this behavior via an information-theoretic approach. By analyzing the correlation distribution and the information flow within the composite system including the qubit subsystem and a noisy environment, it has been found that the subsystem-environment coupling can induce the quasi-periodic entanglement revival. Furthermore, the dynamical relationship among tripartite correlations, bipartite entanglement and local state information is explored, which provides a new insight into the non-Markovian mechanisms during the evolution.

scholarly journals On an atom with a magnetic quadrupole moment subject to harmonic and linear confining potentials

2015 ◽  
Vol 471 (2184) ◽  
pp. 20150362 ◽  
Author(s):  
I. C. Fonseca ◽  
Knut Bakke
Keyword(s):  
External Field ◽  
Electric Field ◽  
Quadrupole Moment ◽  
Coulomb Potential ◽  
Ground State ◽  
Quantum Dynamics ◽  
Quantum Effect ◽  
Angular Frequency ◽  
Quantum Numbers ◽  
Magnetic Quadrupole

The quantum dynamics of an atom with a magnetic quadrupole moment that interacts with an external field subject to harmonic and linear confining potentials is investigated. It is shown that the interaction between the magnetic quadrupole moment and an electric field gives rise to an analogue of the Coulomb potential and, by confining this atom to harmonic and linear confining potentials, a quantum effect characterized by the dependence of the angular frequency on the quantum numbers of the system is obtained. In particular, it is shown that the possible values of the angular frequency associated with the ground state of the system are determined by a third-degree algebraic equation.

scholarly journals On the quantum dynamics of degenerate systems

1925 ◽  
Vol 107 (742) ◽  
pp. 237-246 ◽  
Keyword(s):  
Dynamical Systems ◽  
General Theory ◽  
External Field ◽  
Periodic System ◽  
Quantum Dynamics ◽  
Degrees Of Freedom ◽  
Charged Particles ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Newtonian Dynamics

§1. It is well known that if F i = n i h , i ═ 1, 2, ... (1) be a set of quantum conditions applicable to a class of dynamical systems, then F i must satisfy the definite condition: ∂F i /∂ a ═ 0, (2) where a is a parameter, such as an external field, etc., which is followed to undergo a slow non-systematic variation. In other words, F i must be an “adiabatic invariant” of the class of systems. Burgers has shown, on the basis of Newtonian dynamics, that I i ═ ∫ 0 P i dq i fulfils this condition in the case of a conditionally periodic system of several degrees of freedom where q i p i are separable Hamiltonian co-ordinates, provided the system he non-degenerate, i. e , provided no relation of the form ∑ i s i j ν i = 0 (3) exist between the frequencies ν i , where s i j is an integer, positive or negative, In the case of a system of charged particles, W. Wilson has shown that on the basis of the general theory of relativity, p i should be replaced by π i where π i = p i + e A i , (4)

scholarly journals Stability of the Enhanced Area Law of the Entanglement Entropy

2020 ◽  
Vol 21 (11) ◽  
pp. 3639-3658
Author(s):  
Peter Müller ◽  
Ruth Schulte
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Ground State ◽  
Entanglement Entropy ◽  
Fermi Gas ◽  
Central Idea ◽  
Bipartite Entanglement ◽  
Free Fermi ◽  
Negative Laplacian ◽  
Area Law

Abstract We consider a multi-dimensional continuum Schrödinger operator which is given by a perturbation of the negative Laplacian by a compactly supported potential. We establish both an upper bound and a lower bound on the bipartite entanglement entropy of the ground state of the corresponding quasi-free Fermi gas. The bounds prove that the scaling behaviour of the entanglement entropy remains a logarithmically enhanced area law as in the unperturbed case of the free Fermi gas. The central idea for the upper bound is to use a limiting absorption principle for such kinds of Schrödinger operators.

scholarly journals Quantum Noise from Reduced Dynamics

2016 ◽  
Vol 15 (03) ◽  
pp. 1640003 ◽  
Author(s):  
Bassano Vacchini
Keyword(s):  
Quantum Mechanics ◽  
Quantum Correlation ◽  
Quantum Dynamics ◽  
Degrees Of Freedom ◽  
Composite System ◽  
Quantum Noise ◽  
Interpretation Of Quantum Mechanics ◽  
Statistical Structure ◽  
Master Equation Approach

We consider the description of quantum noise within the framework of the standard Copenhagen interpretation of quantum mechanics applied to a composite system environment setting. Averaging over the environmental degrees of freedom leads to a stochastic quantum dynamics, described by equations complying with the constraints arising from the statistical structure of quantum mechanics. Simple examples are considered in the framework of open system dynamics described within a master equation approach, pointing in particular to the appearance of the phenomenon of decoherence and to the relevance of quantum correlation functions of the environment in the determination of the action of quantum noise.

THE INFLUENCE OF OXYGEN AVAILABILITY ON THE DEGREE OF NITRATE REDUCTION BY SEUDOMONAS DENITRIFICANS

1957 ◽  
Vol 3 (3) ◽  
pp. 505-530 ◽  
Author(s):  
V. B. D. Skerman ◽  
I. C. MacRae
Keyword(s):  
Oxygen Concentration ◽  
Nitrate Reduction ◽  
Direct Relationship ◽  
Critical Level ◽  
No Reduction ◽  
Quantitative Relationship ◽  
Solution Rate ◽  
Pseudomonas Denitrificans ◽  
Precise Data ◽  
Oxygen Solution

An attempt has been made to correlate nitrate reduction by Pseudomonas denitrificans with oxygen concentration in solution.Evidence has been obtained which indicates that nitrate reduction occurs only when the oxygen concentration is below the critical level at which the oxygen utilizing enzymes are saturated. Whilst precise data on the quantitative relationship between nitrate reduction and oxygen reduction at oxygen concentrations between 0 and 0.3 p.p.m. are lacking, it has been clearly established that nitrate reduction occurring in so-called "aerated" solutions is due mainly to the activity of cells deprived of an oxygen supply and that there is a direct relationship between nitrate reduction and the oxygen solution rate. No reduction was detectable at an oxygen concentration above 0.2 p.p.m.It has also been shown that with gas dispersed at the bottom of a fluid the breaking of the foam accumulating on the surface contributes markedly to the oxygen concentration in the solution.Procedures employed in the study are described in detail and implications of results on nitrate reduction in soils have been discussed.

scholarly journals Extreme eigenvalues of Wishart matrices: application to entangled bipartite system

2018 ◽  
Author(s):  
Carlo W. J. Beenakker
Keyword(s):  
Hilbert Spaces ◽  
Matrix Theory ◽  
Minimum Eigenvalue ◽  
Bipartite Entanglement ◽  
Wishart Matrices ◽  
Extreme Eigenvalues ◽  
Bipartite System ◽  
System P ◽  
Random Pure State ◽  
Reduced Density

This article describes the application of random matrix theory (RMT) to the estimation of the bipartite entanglement of a quantum system, with particular emphasis on the extreme eigenvalues of Wishart matrices. It first provides an overview of some spectral properties of unconstrained Wishart matrices before introducing the problem of the random pure state of an entangled quantum bipartite system consisting of two subsystems whose Hilbert spaces have dimensions M and N respectively with N ≤ M. The focus is on the smallest eigenvalue which serves as an important measure of entanglement between the two subsystems. The minimum eigenvalue distribution for quadratic matrices is also considered. The article shows that the N eigenvalues of the reduced density matrix of the smaller subsystem are distributed exactly as the eigenvalues of a Wishart matrix, except that the eigenvalues satisfy a global constraint: the trace is fixed to be unity.

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