Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Journal of Quantum Information

DYNAMICS OF PAIRWISE ENTANGLEMENT IN THE THREE-QUBIT HEISENBERG XX SPIN CHAIN

E. WU, Xiaoan Zhang

Published Dec 1, 2009• 2 citations
Publisher

Abstract

For a three-qubit Heisenberg XX spin chain with the uniform magnetic field and magnetic impurity, dynamic evolution of pairwise entanglement are studied. We show that the phenomenon of entanglement sudden death (ESD) occurs in the evolution of entanglement for some initial states. We also find that magnetic impurity cannot only eliminate the phenomenon of ESD but also induce the ESD effects, which is different from the case of uniform magnetic field where the ESD can be depressed but cannot be eliminated by introducing the uniform magnetic field.

DOI
10.1142/s0219749909005985

Related papers

Dynamics of pairwise entanglement in the four-qubit HeisenbergXXspin chain

Jin‐Liang Guo, He‐Shan Song

We discuss the dynamic evolution of pairwise entanglement in a four-qubit Heisenberg XX spin chain with the periodic boundary condition and the external magnetic field considered. The results show that the so-called entanglement sudden death (ESD) effect can be weakened when introducing the periodic boundary condition and the magnetic impurity. In addition, we also find that the ESD affects the dynamic evolution of entanglement between weakly interacting alternate qubits stronger than that for strongly interacting nearest qubits.

Journal of Modern Optics•Oct 10, 2008•2 citations

Sudden Death, Birth and Stable Entanglement in a Two-Qubit Heisenberg XY Spin Chain

Shan Chuan-Jia, Cheng Wei-Wen, Tang-Kun Liu +2 more

Taking the decoherence effect due to population relaxation into account, we investigate the entanglement properties for two qubits in the Heisenberg XY interaction and subject to an external magnetic Geld. It is found that the phenomenon of entanglement sudden death (ESD) as well as sudden birth (ESB) appear during the evolution process for particular initial states. The influence of the external magnetic Geld and the spin environment on ESD and ESB are addressed in detail. It is shown that the concurrence, a measure of entanglement, can be controlled by tuning the parameters of the spin chain, such as the anisotropic parameter, external magnetic Geld, and the coupling strength with their environment. In particular, we Gnd that a critical anisotropy constant exists, above which ESB vanishes while ESD appears. It is also notable that stable entanglement, which is independent of different initial states of the qubits, occurs even in the presence of decoherence.

arXiv:0807.3208•Chinese Physics Letters•Sep 1, 2008•20 citations

Decoherence Effect in An Anisotropic Two-Qubit Heisenberg XYZ Model with Inhomogeneous Magnetic Field

Tao Chen, Shan Chuan-Jia, Li Jin-Xing +3 more

Taking the decoherence effect into account, the entanglement evolution of a two-qubit anisotropic Heisenberg XYZ chain in the presence of inhomogeneous magnetic field is investigated. The time evolution of concurrence is studied for the initial state cos θ |01⟩ +sin θ|10⟩ at zero temperature. The influences of inhomogeneous magnetic field, anisotropic parameter and decoherence on entanglement dynamic are addressed in detail, and a concurrence formula of the steady state is found. It is shown that the entanglement sudden death (ESD) and entanglement sudden birth (ESB) appear with the decoherence effect, and the stable concurrence depends on the uniform magnetic field B , anisotropic parameter Δ and environment coupling strength γ, which is independent of different initial states and nonuniform magnetic field b.

Communications in Theoretical Physics•Jun 1, 2010•5 citations

Entanglement sudden death induced by the Dzialoshinskii–Moriya interaction

Zeng Hong-Fang, Shao Bin, Linguang Yang +2 more

In this paper, we study the entanglement dynamics of two-spin Heisenberg XYZ model with the Dzialoshinskii–Moriya (DM) interaction. The system is initially prepared in the Werner state. The effects of purity of the initial state and DM coupling parameter on the evolution of entanglement are investigated. The necessary and sufficient condition for the appearance of the entanglement sudden death (ESD) phenomenon has been deduced. The result shows that the ESD always occurs if the initial state is sufficiently impure for the given coupling parameter or the DM interaction is sufficiently strong for the given initial state. Moreover, the critical values of them are calculated.

Chinese Physics B•Jul 31, 2009•15 citations

Quantum phase transition and entanglement in Heisenberg XX spin chain with impurity

Shirong Chen, Yun‐Jie Xia, Man Zhong-Xiao

In this paper, we study the quantum phase transition and the effect of impurity on the thermal entanglement between any two lattices in three-qubit Heisenberg XX chain in a uniform magnetic field. We show that the quantum phase transition always appears when impurity parameter is an arbitrary constant and unequal to zero, the external magnetic field and impurity parameters have a great effect on it. Also, there exists a relation between the quantum phase transition and the entanglement. By modulating the temperature, magnetic field and the impurity parameters, the entanglement between any two lattices can exhibit platform-like behaviour, which can be used to realize entanglement switch.

Chinese Physics B•May 1, 2010•11 citations

EFFECTS OF ANISOTROPY ON DYNAMICS OF PAIRWISE ENTANGLEMENT IN THE FOUR-QUBIT HEISENBERG XXZ MODEL

Jin‐Liang Guo, He‐Shan Song

We investigate the effects of anisotropy on the dynamic evolution of pairwise entanglement in the four-qubit Heisenberg XXZ model. The entanglement between the nearest-neighbor and the next nearest-neighbor qubits are calculated by making use of concurrence. Our results show that the sudden death effect can be weakened when introducing the anisotropy Δ. In addition, we also find that the anisotropy Δ can protect the entanglement between the nearest-neighbor qubits from being completely destroyed by the intrinsic decoherence, but it cannot do this for the entanglement between the next nearest-neighbor qubits.

International Journal of Quantum Information•Oct 1, 2009•0 citations
For a three-qubit Heisenberg XX spin chain with the uniform magnetic field and magnetic impurity, dynamic evolution of pairwise entanglement are studied. We show that the phenomenon of entanglement sudden death (ESD) occurs in the evolution of entanglement for some initial states. We also find that magnetic impurity cannot only eliminate the phenomenon of ESD but also induce the ESD effects, which is different from the case of uniform magnetic field where the ESD can be depressed but cannot be eliminated by introducing the uniform magnetic field.
We discuss the dynamic evolution of pairwise entanglement in a four-qubit Heisenberg XX spin chain with the periodic boundary condition and the external magnetic field considered. The results show that the so-called entanglement sudden death (ESD) effect can be weakened when introducing the periodic boundary condition and the magnetic impurity. In addition, we also find that the ESD affects the dynamic evolution of entanglement between weakly interacting alternate qubits stronger than that for strongly interacting nearest qubits.
Taking the decoherence effect due to population relaxation into account, we investigate the entanglement properties for two qubits in the Heisenberg XY interaction and subject to an external magnetic Geld. It is found that the phenomenon of entanglement sudden death (ESD) as well as sudden birth (ESB) appear during the evolution process for particular initial states. The influence of the external magnetic Geld and the spin environment on ESD and ESB are addressed in detail. It is shown that the concurrence, a measure of entanglement, can be controlled by tuning the parameters of the spin chain, such as the anisotropic parameter, external magnetic Geld, and the coupling strength with their environment. In particular, we Gnd that a critical anisotropy constant exists, above which ESB vanishes while ESD appears. It is also notable that stable entanglement, which is independent of different initial states of the qubits, occurs even in the presence of decoherence.
Taking the decoherence effect into account, the entanglement evolution of a two-qubit anisotropic Heisenberg XYZ chain in the presence of inhomogeneous magnetic field is investigated. The time evolution of concurrence is studied for the initial state cos θ |01⟩ +sin θ|10⟩ at zero temperature. The influences of inhomogeneous magnetic field, anisotropic parameter and decoherence on entanglement dynamic are addressed in detail, and a concurrence formula of the steady state is found. It is shown that the entanglement sudden death (ESD) and entanglement sudden birth (ESB) appear with the decoherence effect, and the stable concurrence depends on the uniform magnetic field B , anisotropic parameter Δ and environment coupling strength γ, which is independent of different initial states and nonuniform magnetic field b.
In this paper, we study the entanglement dynamics of two-spin Heisenberg XYZ model with the Dzialoshinskii–Moriya (DM) interaction. The system is initially prepared in the Werner state. The effects of purity of the initial state and DM coupling parameter on the evolution of entanglement are investigated. The necessary and sufficient condition for the appearance of the entanglement sudden death (ESD) phenomenon has been deduced. The result shows that the ESD always occurs if the initial state is sufficiently impure for the given coupling parameter or the DM interaction is sufficiently strong for the given initial state. Moreover, the critical values of them are calculated.
In this paper, we study the quantum phase transition and the effect of impurity on the thermal entanglement between any two lattices in three-qubit Heisenberg XX chain in a uniform magnetic field. We show that the quantum phase transition always appears when impurity parameter is an arbitrary constant and unequal to zero, the external magnetic field and impurity parameters have a great effect on it. Also, there exists a relation between the quantum phase transition and the entanglement. By modulating the temperature, magnetic field and the impurity parameters, the entanglement between any two lattices can exhibit platform-like behaviour, which can be used to realize entanglement switch.
We investigate the effects of anisotropy on the dynamic evolution of pairwise entanglement in the four-qubit Heisenberg XXZ model. The entanglement between the nearest-neighbor and the next nearest-neighbor qubits are calculated by making use of concurrence. Our results show that the sudden death effect can be weakened when introducing the anisotropy Δ. In addition, we also find that the anisotropy Δ can protect the entanglement between the nearest-neighbor qubits from being completely destroyed by the intrinsic decoherence, but it cannot do this for the entanglement between the next nearest-neighbor qubits.