TYPICAL BEHAVIOR OF THE GLOBAL ENTANGLEMENT OF AN OPEN MULTIQUBIT SYSTEM IN A NON-MARKOVIAN REGIMEN

We investigate the decay of the global entanglement, due to decoherence, of multiqubit systems interacting with a reservoir in a non-Markovian regime. We assume that during the decoherence process each qubit of the system interacts with its own, independent environment. Most previous works on this problem focused on particular initial states or families of initial states amenable of analytical treatment. Here we determine numerically the typical, average behavior of the system corresponding to random initial pure states uniformly distributed (in the whole Hilbert space of n-qubit pure states) according to the Haar measure. We study systems consisting of 3, 4, 5, and 6 qubits. In each case we consider also the entanglement dynamics corresponding to important particular initial states, such as the GHZ states or multiqubit states maximizing the global entanglement, and determine in which cases any of these states is representative of the average behavior associated with general initial states.

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Classical-hidden-variable description for entanglement dynamics of two-qubit pure states

Physical Review A ◽

10.1103/physreva.95.062105 ◽

2017 ◽

Vol 95 (6) ◽

Cited By ~ 2

Author(s):

L. S. Silveira ◽

R. M. Angelo

Keyword(s):

Entanglement Dynamics ◽

Hidden Variable ◽

Pure States

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CLASSICAL TENSORS AND QUANTUM ENTANGLEMENT I: PURE STATES

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887810004300 ◽

2010 ◽

Vol 07 (03) ◽

pp. 485-503 ◽

Cited By ~ 9

Author(s):

P. ANIELLO ◽

J. CLEMENTE-GALLARDO ◽

G. MARMO ◽

G. F. VOLKERT

Keyword(s):

Hilbert Space ◽

Symplectic Geometry ◽

Vector Fields ◽

Riemannian Metric ◽

Inner Product ◽

Tensor Fields ◽

Metric Tensor ◽

Separable States ◽

Pure States ◽

Complex Projective

The geometrical description of a Hilbert space associated with a quantum system considers a Hermitian tensor to describe the scalar inner product of vectors which are now described by vector fields. The real part of this tensor represents a flat Riemannian metric tensor while the imaginary part represents a symplectic two-form. The immersion of classical manifolds in the complex projective space associated with the Hilbert space allows to pull-back tensor fields related to previous ones, via the immersion map. This makes available, on these selected manifolds of states, methods of usual Riemannian and symplectic geometry. Here, we consider these pulled-back tensor fields when the immersed submanifold contains separable states or entangled states. Geometrical tensors are shown to encode some properties of these states. These results are not unrelated with criteria already available in the literature. We explicitly deal with some of these relations.

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ENTANGLEMENT DYNAMICS IN FINITE QUDIT CHAIN IN CONSISTENT MAGNETIC FIELD

International Journal of Quantum Information ◽

10.1142/s0219749912500682 ◽

2012 ◽

Vol 10 (06) ◽

pp. 1250068 ◽

Cited By ~ 3

Author(s):

E. A. IVANCHENKO

Keyword(s):

Magnetic Field ◽

Entanglement Dynamics ◽

Von Neumann ◽

Magnetic Field Modulation ◽

Entanglement Measures ◽

Analytical Formulae ◽

Initial States ◽

Von Neumann Equation ◽

Field Modulation ◽

The Magnetic Field

Based on the Liouville–von Neumann equation, we obtain a closed system of equations for the description of a qutrit or coupled qutrits in an arbitrary, time-dependent, external magnetic field. The dependence of the dynamics on the initial states and the magnetic field modulation is studied analytically and numerically. We compare the relative entanglement measure's dynamics in bi-qudits with permutation particle symmetry. We find the magnetic field modulation which retains the entanglement in the system of two coupled qutrits. Analytical formulae for the entanglement measures in finite chains from two to six qutrits or three quartits are presented.

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ENTANGLEMENT DYNAMICS OF TWO QUBITS COUPLED TO SQUEEZED DISSIPATIVE ENVIRONMENTS

Modern Physics Letters B ◽

10.1142/s0217984910024948 ◽

2010 ◽

Vol 24 (26) ◽

pp. 2635-2645

Author(s):

CHUAN-JIA SHAN ◽

TAO CHEN ◽

JI-BING LIU ◽

WEI-WEN CHENG ◽

TANG-KUN LIU ◽

...

Keyword(s):

Steady State ◽

Sudden Death ◽

Entangled States ◽

Entanglement Sudden Death ◽

Entanglement Dynamics ◽

Initial Product ◽

System Parameters ◽

Initial States ◽

Dissipative Environments ◽

Degree Of Entanglement

By analytically solving the Lindblad form of the master equation, we investigate entanglement dynamics of two qubits coupled via the XY interaction, where each qubit is interacting with an independent reservoir with the squeezing parameters and squeezing angles. In the weak-squeezed reservoir, we show that the entanglement sudden death and entanglement sudden birth will happen for various entangled states. Some initial product states evolve into entangled ones, initially entangled states lose completely or partially their entanglement. The effects of varying the degree of entanglement of the initial states, the spin chain system parameters and different values of the degree of squeezing on the sudden death, revival and birth times are analyzed in detail. We also see that the steady state concurrence appears in the squeezed dissipative environments, which is affected by both the system parameters and the degree of squeezing.

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Dynamics of Quantum Correlations in a Qubit-Oscillator System Interacting via a Dissipative Bath

Open Systems & Information Dynamics ◽

10.1142/s1230161220500043 ◽

2020 ◽

Vol 27 (01) ◽

pp. 2050004

Author(s):

R. Badveli ◽

V. Jagadish ◽

S. Akshaya ◽

R. Srikanth ◽

F. Petruccione

Keyword(s):

Harmonic Oscillator ◽

Numerical Simulations ◽

Dipole Interaction ◽

Quantum Correlations ◽

Entanglement Dynamics ◽

Lindblad Equation ◽

Oscillator System ◽

Microscopic Derivation ◽

Initial States ◽

Classical Correlations

The entanglement dynamics in a bipartite system consisting of a qubit and a harmonic oscillator interacting only through their coupling with the same bath is studied. The considered model assumes that the qubit is coupled to the bath via the Jaynes-Cummings interaction, whilst the position of the oscillator is coupled to the position of the bath via a dipole interaction. We give a microscopic derivation of the Gorini–Kossakowski–Sudarshan–Lindblad equation for the considered model. Based on the Kossakowski matrix, we show that non-classical correlations including entanglement can be generated by the considered dynamics. We then analytically identify specific initial states for which entanglement is generated. This result is also supported by our numerical simulations.

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Atomic motion and dipole–dipole effects on the stability of atom–atom entanglement in Markovian/non-Markovian reservoir

Modern Physics Letters A ◽

10.1142/s0217732319500779 ◽

2019 ◽

Vol 34 (10) ◽

pp. 1950077 ◽

Cited By ~ 3

Author(s):

S. Golkar ◽

M. K. Tavassoly

Keyword(s):

Weak Coupling ◽

Initial Conditions ◽

Dynamical Behavior ◽

Dipole Interaction ◽

Zero Temperature ◽

Entanglement Dynamics ◽

Entanglement Protection ◽

Initial States ◽

The Stability ◽

Suitable Measure

In this paper, we consider the entanglement dynamics of two identical qubits (two-level atoms) accompanied by dipole–dipole interaction within a common reservoir in the strong and weak coupling regimes. We suppose that the qubits move in the reservoir which is at zero temperature. Using the time-dependent Schrödinger equation, the state vector of the qubits-reservoir system is obtained by which we can evaluate the concurrence as a suitable measure of entanglement between the two qubits. The results show that by choosing special initial conditions for the qubits, a different dynamical behavior of entanglement is visible in such a way that entanglement protection occurs. Also, we find that the qubit motion in the absence of dipole–dipole interaction leads to preservation or at least more slowly decay of entanglement. However, in the presence of dipole–dipole interaction with the movement of qubits, different results can be observed which depend on the initial states of the qubits, i.e. entanglement may or may not be protected.

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MULTI-QUBIT TRIGONOMETRIC STATES AND ENTANGLEMENT MONOTONES

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887812610051 ◽

2012 ◽

Vol 09 (06) ◽

pp. 1261005

Author(s):

ANDRZEJ M. FRYDRYSZAK

Keyword(s):

Point Of View ◽

Physical Point ◽

Ghz States ◽

The Family ◽

Pure States ◽

Werner States

The formalism of functions of commuting nilpotent variables allows to describe multi-qubit pure states and their entanglement. The family of states defined by the generalized trigonometric η-functions is specially interesting from mathematical and physical point of view (it covers the set of physically interesting states, including: Werner states, cluster Werner states, GHZ states etc.). We analyze the behavior of two recently proposed symmetric entanglement monotones on the trigonometric states.

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Entanglement Dynamics of Arbitrary Two-Qubit Pure States under Amplitude and Phase Damping Channels

Chinese Physics Letters ◽

10.1088/0256-307x/28/2/020308 ◽

2011 ◽

Vol 28 (2) ◽

pp. 020308 ◽

Cited By ~ 2

Author(s):

Feng-Jian Jiang ◽

Ming-Jun Shi ◽

Jiang-Feng Du

Keyword(s):

Entanglement Dynamics ◽

Phase Damping ◽

Pure States

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Entanglement of Three-Qubit Random Pure States

Entropy ◽

10.3390/e20100745 ◽

2018 ◽

Vol 20 (10) ◽

pp. 745 ◽

Cited By ~ 7

Author(s):

Marco Enríquez ◽

Francisco Delgado ◽

Karol Życzkowski

Keyword(s):

Haar Measure ◽

Probability Distributions ◽

Classical Communication ◽

Polynomial Invariants ◽

Analytical Work ◽

Pure States ◽

Random State

We study entanglement properties of generic three-qubit pure states. First, we obtain the distributions of both the coefficients and the only phase in the five-term decomposition of Acín et al. for an ensemble of random pure states generated by the Haar measure on U ( 8 ) . Furthermore, we analyze the probability distributions of two sets of polynomial invariants. One of these sets allows us to classify three-qubit pure states into four classes. Entanglement in each class is characterized using the minimal Rényi-Ingarden-Urbanik entropy. Besides, the fidelity of a three-qubit random state with the closest state in each entanglement class is investigated. We also present a characterization of these classes in terms of the corresponding entanglement polytope. The entanglement classes related to stochastic local operations and classical communication (SLOCC) are analyzed as well from this geometric perspective. The numerical findings suggest some conjectures relating some of those invariants with entanglement properties to be ground in future analytical work.

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