Shan Chuan-Jia

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

1College of Physics and Electronic Science, Hubei Normal University, Huangshi 435002, China 2Department of Physics, Huazhong University of Science and Technology, Wuhan 430074, China 3State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan, 430071, China (Dated: August 31, 2008) Abstract Taking the decoherence effect due to population relaxation int account, we investigate the entanglement properties for two qubits in the Heisenberg XY interaction a nd subject to an external magnetic field. It is found that the phenomenon of entanglement sudden death (E SD) as well as sudden birth(ESB) appear during the evolution process for particular initial states . The influence of the external magnetic field and the spin environment on ESD and ESB are addressed in detail. I t 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 field, and the coupling streng th with their environment. In particular, we find that a critical anisotropy constant exists, above which ESB vanishes while ESD appears. It is also notable that stable entanglement, which is independent of differen t initial states of the qubits, occurs even in the presence of decoherence.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 field. 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 field 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 field, and the coupling strength with their environment. In particular, we find 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.

Master equation describing the diffusion process for a coherent state

The evolution of a pure coherent state into a chaotic state is described very well by a master equation, as is validated via an examination of the coherent states evolution during the diffusion process, fully utilizing the technique of integration within an ordered product (IWOP) of operators. The same equation also describes a limitation that maintains the coherence in a weak diffusion process, i.e., when the dissipation is very weak and the initial average photon number is large. This equation is dρ/ dt = −κ[a+aρ −a+ρa − aρa+ + ρaa+]. The physical difference between this diffusion equation and the better-known amplitude damping master equation is pointed out.

Entanglement evolution in an anisotropic two-qubit Heisenberg XYZ model with Dzyaloshinskii–Moriya interaction

This paper investigates the entanglement evolution of a two-qubit anisotropic Heisenberg XYZ chain in the presence of Dzyaloshinskii–Moriya interaction. The time evolution of the concurrence is studied for the initial pure entangled states cos θ |00 + sin θ |11 and cos |01 + sin |10 at zero temperature. The influences of Dzyaloshinskii–Moriya interaction D, anisotropic parameter Δ and environment coupling strength γ on entanglement evolution are analysed in detail. It is found that the effect of noisy environment obviously suppresses the entanglement evolution, and the Dzyaloshinskii–Moriya interaction D acts on the time evolution of entanglement only when the initial state is cos |01 + sin |10. Finally, a formula of steady state concurrence is obtained, and it is shown that the stable concurrence, which is independent of different initial states and Dzyaloshinskii–Moriya interaction D, depends on the anisotropic parameter Δ and the environment coupling strength γ.

Entanglement Dynamics of Two-Qubit System in Different Types of Noisy Channels

In this paper, we study entanglement dynamics of a two-qubit extended Werner-like state locally interacting with independent noisy channels, i.e., amplitude damping, phase damping, and depolarizing channels. We show that the purity of initial entangled state has direct impacts on the entanglement robustness in each noisy channel. That is, if the initial entangled state is prepared in mixed instead of pure form, the state may exhibit entanglement sudden death (ESD) and/or be decreased for the critical probability at which the entanglement disappear.

Entanglement in One-Dimensional Random XY Spin Chain with Dzyaloshinskii–Moriya Interaction

The impurities of exchange couplings, external magnetic fields and Dzyaloshinskii–Moriya (DM) interaction considered as Gaussian distribution, and the entanglement in one-dimensional random XY spin systems is investigated by the method of solving the different spin-spin correlation functions and the average magnetization per spin. The entanglement dynamics at central locations of ferromagnetic and antiferromagnetic chains have been studied by varying the three impurities and the strength of DM interaction. (i) For the ferromagnetic spin chain, the weak DM interaction can improve the amount of entanglement to a large value, and the impurities have the opposite effect on the entanglement below and above critical DM interaction. (ii) For the antiferromagnetic spin chain, DM interaction can enhance the entanglement to a steady value. Our results imply that DM interaction strength, the impurity and exchange couplings (or magnetic field) play competing roles in enhancing quantum entanglement.C. J. Shan, W. W. Cheng, T. K. Liu, Y. X. Huang, and H. Li College of Physics and Electronic Science, Hubei Normal University, Huangshi 435002, China (Dated: August 27, 2008) Abstract The impurities of exchange couplings, external magnetic fie lds and Dzyaloshinskii–Moriya (DM) interaction considered as Gaussian distribution, the entanglem ent in one-dimensional random XY spin systems is investigated by the method of solving the different spinspin correlation functions and the average magnetization per spin. The entanglement dynamics at central l oc tions of ferromagnetic and antiferromagnetic chains have been studied by varying the three impurities and the strength of DM interaction. (i) For ferromagnetic spin chain, the weak DM interaction can improve the amount of entanglement to a large value, and the impurities have the opposite effect on the entanglem ent below and above critical DM interaction. (ii) For antiferromagnetic spin chain, DM interaction can e nhance the entanglement to a steady value. Our results imply that DM interaction strength, the impurity an d exchange couplings (or magnetic field) play competing roles in enhancing quantum entanglement.The impurities of exchange couplings, external magnetic fields and Dzyaloshinskii--Moriya (DM) interaction considered as Gaussian distribution, the entanglement in one-dimensional random

Entanglement Dynamics and Bell Violations of Two Atoms in Tavis–Cummings Model with Phase Decoherence

XY

Entanglement properties in a system of a pairwise entangled state

spin systems is investigated by the method of solving the different spin-spin correlation functions and the average magnetization per spin. The entanglement dynamics at central locations of ferromagnetic and antiferromagnetic chains have been studied by varying the three impurities and the strength of DM interaction. (i) For ferromagnetic spin chain, the weak DM interaction can improve the amount of entanglement to a large value, and the impurities have the opposite effect on the entanglement below and above critical DM interaction. (ii) For antiferromagnetic spin chain, DM interaction can enhance the entanglement to a steady value. Our results imply that DM interaction strength, the impurity and exchange couplings (or magnetic field) play competing roles in enhancing quantum entanglement.

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

X iv :0 80 8. 37 09 v1 [ qu an tph ] 27 A ug 2 00 8 Entanglement dynamics and Bell Violations of two atoms in Tavis-Cummings model with phase decoherence ∗ C. J. Shan†,1 W. W. Cheng, 1 T. K. Liu‡,1 D. J. Guo, 2 and Y. J. Xia2 1College of Physics and Electronic Science, Hubei Normal University, Huangshi 435002, China 2Department of Physics, Qufu Normal University, Qufu 273165, China (Dated: August 27, 2008) Abstract Considering the dipole-dipole coupling intensity between two atoms and the field in the Fock state, the entanglement dynamics between two atoms that are initially entangled in the system of two two-level atoms coupled to a single mode cavity in the presence of phase decoh erence has been investigated. The two-atom entanglement appears with periodicity without considerin g phase decoherence, however, the phase decoherence causes the decay of entanglement between two atoms, with the increasing of the phase decoherence coefficient, the entanglement will quickly become a constan t v lue, which is affected by the two-atom initial state, Meanwhile the two-atom quantum state will forev er stay in the maximal entangled state when the initial state is proper even in the presence of phase decoher enc . On the other hand, the Bell violation and the entanglement does not satisfy the monotonous relation, a large Bell violation implies the presence of a large amount of entanglement under certain conditions, whi le a large Bell violation corresponding to a little amount of entanglement in certain situations. However, the violation of Bell-CHSH inequality can reach the maximal value if two atoms are in the maximal entangled st ate, or vice versa.Considering the dipole-dipole coupling intensity between two atoms and the field in the Fock state, the entanglement dynamics between two atoms that are initially entangled in the system of two two-level atoms coupled to a single mode cavity in the presence of phase decoherence has been investigated. The two-atom entanglement appears with periodicity without considering phase decoherence, however, the phase decoherence causes the decay of entanglement between two atoms, with the increasing of the phase decoherence coefficient, the entanglement will quickly become a constant value, which is affected by the two-atom initial state. Meanwhile the two-atom quantum state will forever stay in the maximal entangled state when the initial state is proper even in the presence of phase decoherence. On the other hand, the Bell violation and the entanglement do not satisfy the monotonous relation, a large Bell violation implies the presence of a large amount of entanglement under certain conditions, while a large Bell violation corresponds to a little amount of entanglement in certain situations. However, the violation of Bell-CHSH inequality can reach the maximal value if two atoms are in the maximal entangled state, or vice versa.

Sudden birth versus sudden death of entanglement for the extended Werner-like state in a dissipative environment

Based on the quantum information theory, this paper has investigated the entanglement properties of a system which is composed of the two entangled two-level atoms interacting with the two-mode entangled coherent fields. The influences of the strength of light field and the two parameters of entanglement between the two-mode fields on the field entropy and on the negative eigenvalues of partial transposition of density matrix are discussed by using numerical calculations. The result shows that the entanglement properties in a system of a pairwise entangled states can be controlled by appropriately choosing the two parameters of entanglement between the two-mode entangled coherent fields and the strength of two light fields respectively.

Entanglement control in one-dimensional s = 1/2 random XY spin chain

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.