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

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 △ and environment coupling strength γ, which is independent of different initial states and nonuniform magnetic field b.     

Avoiding the decay of entanglement for coupling two-qubit system interacting with a non-Markov environment

The entanglement evolution of the coupled qubits interacting with a non-Markov environment is investigated in terms of concurrence.The results show that the entanglement of the quantum systems depends not only on the initial state of the system but also on the coupling between the qubit and the environment.For the initial state （|00 ± |11） /2^1/2,the coupled qubits will always been in the maximum entangled state under an asymmetric coupling.For the initial state （|01 ± |10） /2^1/2,in contrast,the entangling degree of the coupled qubits is always equal to unity and does not depend on the evolving time under the symmetric coupling.We find that the stronger the interaction between the qubits is,the better the struggle against the entanglement sudden death is.     

Effects of Anisotropy on Entanglement in a Two-Qubit Heisenberg XYZ Chain with Intrinsic Decoherence

Taking the intrinsic decoherence effect into account, the entanglement ofa two-qubit anisotropic Heisenberg XYZ chain in the presence of the Dzyaloshinski Moriya （DM） anisotropic antisymetric interaction is investigated in this paper. Concurrence, the measurement of entanglement, is calculated. Compared with the anisotropic in XY plane, the DM interaction is another kind of anisotropic antisymmetrie exchange interaction. It is shown that the intrinsic decoherence obviously suppresses the time evolution of the entanglement. The DM interaction only acts on the time evolution of the entanglement when the initial state is [ψ（0）〉 = cosα｜01〉 ＋ sinα｜10〉 and weakens the degree of entanglement. The anisotropic in XY plane merely impacts on the time evolution of the entanglement when the system ＆ initially in a state ｜ψ（0）〉 = cos α｜00〉 ＋ sin α｜11 〉. The sufficiently weak anisotropic in XY plane can effectively enhance the degree of entanglement.     

The entanglement between two isolated atoms in double mode--mode competition model

Extending the double Jaynes--Cummings model to a more complicated case where the mode--mode competition is considered, we investigate the entanglement character of two isolated atoms by means of concurrence, and discuss the dependence of atom--atom entanglement on the different initial state and the relative coupling strength between the atom and the corresponding cavity field. The results show that the amplitude and the period of the atom--atom entanglement evolution can be controlled by the choice of initial state and relative coupling strength, respectively. We find that the phenomenon of entanglement sudden death (ESD) is sensitive to the initial conditions. The length of the time interval for zero entanglement depends not only on the initial degree of entanglement between two atoms but also on the relative coupling strength of atom--field interaction. The ESD effect can be weakened by enhancing the mode--mode competition between the three- and single-photon processes.     

Entanglement of two Jaynes-Cummings atoms in single-excitation space

We study the entanglement dynamics of two atoms coupled to their own Jaynes-Cummings cavities in single-excitation space.Here,we use concurrence to measure atomic entanglement,and consider the Bell-like states to be initial states.Our analysis suggests that collapse and revival take place in entanglement dynamics.The physical mechanism behind entanglement dynamics is periodic information and energy exchange between atoms and light fields.For the initial Bell-like states,evolutionary periodicity of the atomic entanglement can only be found if the ratio of the two atom-cavity coupling strengths is a rational number.Also,whether there is a time translation between two kinds of initial Bel-like state depends on odd versus even numbers of the coupling strength ratio.     

Entanglement sudden death induced by the Dzialoshinskii--Moriya interaction

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.     

Quantum correlation dynamics in a two-qubit Heisenberg XY Z model with decoherence

Quantum correlation dynamics in an anisotropic Heisenberg XY Z model under decoherence is investigated by making use of concurrence C and quantum discord(QD).Firstly,we show that both the concurrence and QD exhibit oscillation with time whereas a remarkable difference between them is presented:there is an "entanglement intermittently sudden death" phenomenon in the concurrence but not in the QD,which is valid for all the initial states of this system.Also,the interval time of entanglement sudden death is found to be strongly dependent on the initial states,the inhomogeneous magnetic field b and the anisotropic parameter ?.Then,it implies that the steady concurrence and QD can be obtained in the long-time limit,which means that the environmental decoherence cannot entirely destroy the quantum correlation,the variation of the uniform magnetic field B and the anisotropic parameter can change the magnitude of the steady concurrence and QD evidently whereas the parameter b cannot.In addition,based on the analysis of the steady concurrence and QD with t →∞,we give the reason why the magnitude of the steady concurrence and QD is so complicated with the change of the parameters B and △,whereas the parameter b is independent of the steady concurrence and QD.     

Effects of Pure Dzyaloshinskii-Moriya Interaction with Magnetic Field on Entanglement in Intrinsic Decoherence

We investigate the effects of pure Dzyaloshinskii-Moriya(DM) interaction with magnetic field on entanglement in intrinsic decoherence,assuming that the system is initially in four Bell states |φ± =(|00 ± |11)/2~(1/2) and|ψ± =(|01) ± |10)/2~(1/2) respectively.It is found that if the system is initially in the state ρ1(0) = |φ+φ+|,the entanglement can obtain its maximum when the DM interaction vector D is in the plane of XOZ and magnetic field B = B_y with the infinite time t,moreover the entanglement is independent of B_y and t when B_y is perpendicular to D.In addition,we obtain similar results when the system is initially in the states ρ2(0) =|φ-φ-| or ρ3(0) = |ψ+ψ+|.However,we find that if the system is initially in the state ρ4(0) =|ψ-ψ-|,the entanglement can obtain its maximum for infinite t,when the DM vector is in the plane of YOZ,XOZ,or XOY,with the magnetic field parallel to X,Y,or Z axis,respectively.Moreover,when the axial B is perpendicular to D for the initial state ρ4(0),the negativity oscillates with time t and reaches a stabie value,the larger the value of B is,the greater the stable value is,and the shorter the oscillation time of the negativity is.Thus we can adjust the direction and value of the external magnetic field to obtain the maximal entanglement,and avoid the adverse effects of external environment in some initial state.This is feasible within the current experimental technology.     

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

In this paper, we investigate the dynamical behaviour of entanglement in terms of concurrence in a bipartite system subjected to an external magnetic field under the action of dissipative environments in the extended Werner-like initial state. The interesting phenomenon of entanglement sudden death as well as sudden birth appears during the evolution process. We analyse in detail the effect of the purity of the initial entangled state of two qubits via Heisenberg XY interaction on the apparition time of entanglement sudden death and entanglement sudden birth. Furthermore, the conditions on the conversion of entanglement sudden death and entanglement sudden birth can be generalized when the initial entangled state is not pure. In particular, a critical purity of the initial mixed entangled state exists, above which entanglement sudden birth vanishes while entanglement sudden death appears. It is also noticed that stable entanglement, which is independent of different initial states of the qubits (pure or mixed state), occurs even in the presence of decoherence. These results arising from the combination of the extended Werner-like initial state and dissipative environments suggest an approach to control and enhance the entanglement even after purity induced sudden birth, death and revival.     

Concurrence evolution of two qubits coupled with one-mode cavity separately

The concurrence evolution of two qubits coupled with one-mode cavity separately is investigated exactly without adopting the rotating-wave approximation. The results show that for the resonant case, the concurrence evolution behaviour of the system is similar to that of the Markovian case when the coupling strength is weak, while the concurrence vanishes in a finite time and might revive fractional initial entanglement before it permanently vanishes when the coupling strength is strong. And for the detuning case, the entanglement could periodically recover after complete disentanglement. These results are quite different from those of system subjected to Jaynes--Cummings model.     

Entanglement of a two-qubit anisotropic Heisenberg XYZ chain in nonuniform magnetic fields with intrinsic decoherence

Taking the intrinsic decoherence effect into account, this paper investigates the entanglement of a two-qubit anisotropic Heisenberg XYZ model in the presence of nonuniform external magnetic fields by employing the concurrence as entanglement measure. It is found that both the intrinsic decoherence and the anisotropy of the system give a significant suppression to the entanglement. Moreover it finds that the initial state of the system plays an important role in the time evolution of the entanglement, which means that the entanglement of the system is independent of the nonuniformity and uniformity of the magnetic field when the system is in the initial state ｜ψ （0）） = ｜00） and [ψ′ （0）） = m ｜01） ＋ n ｜10）, respectively.     

Effects of phase decoherence on the entanglement of a two-qubit anisotropic Heisenberg XYZ chain with an in-plane magnetic field

We investigate the phase decoherence effects on the entanglement of a two-qubit anisotropic Heisenberg model with a nonuniform magnetic field in the x–z-plane. As a measure of the entanglement, the concurrence of the system is calculated. It is shown that when the magnetic field is along the z-axis, the nonuniform and uniform components of the field have no influence on the entanglement for the cases of and , respectively. But when the magnetic field is not along the z-axis, both the uniform and the nonuniform components of the field will introduce the decoherence effects. It is found that the effects of the Heisenberg chain's anisotropy in the Z-direction on the entanglement are dependent on the direction of the field. Moreover, the larger the initial concurrence is, the higher value it will exhibit during the time evolution of the system for a proper set of the parameters ν, Δ, θ, γ , B and b.     

Influence of dephasing on the entanglement teleportation via a two-qubit Heisenberg XYZ system

We study the entanglement dynamics of an anisotropic two-qubit Heisenberg XYZ system in the presence of intrinsic decoherence. The usefulness of such a system for performance of the quantum teleportation protocol T₀\mathcal{T}_0 and entanglement teleportation protocol T₁\mathcal{T}_1 is also investigated. The results depend on the initial conditions and the parameters of the system. The roles of system parameters such as the inhomogeneity of the magnetic field b and the spin-orbit interaction parameter D, in entanglement dynamics and fidelity of teleportation, are studied for both product and maximally entangled initial states of the resource. We show that for the product and maximally entangled initial states, increasing D amplifies the effects of dephasing and hence decreases the asymptotic entanglement and fidelity of the teleportation. For a product initial state and specific interval of the magnetic field B, the asymptotic entanglement and hence the fidelity of teleportation can be improved by increasing B. The XY and XYZ Heisenberg systems provide a minimal resource entanglement, required for realizing efficient teleportation. Also, in the absence of the magnetic field, the degree of entanglement is preserved for the maximally entangled initial states $\left| {\psi \left. {\left( 0 \right)} \right\rangle = \frac{1} {{\sqrt 2 }}\left( {\left| {\left. {00} \right\rangle \pm } \right|\left. {11} \right\rangle } \right)} \right.$\left| {\psi \left. {\left( 0 \right)} \right\rangle = \frac{1} {{\sqrt 2 }}\left( {\left| {\left. {00} \right\rangle \pm } \right|\left. {11} \right\rangle } \right)} \right.. The same is true for the maximally entangled initial states $\left| {\psi \left. {\left( 0 \right)} \right\rangle = \frac{1} {{\sqrt 2 }}\left( {\left| {\left. {01} \right\rangle \pm } \right|\left. {10} \right\rangle } \right)} \right.$\left| {\psi \left. {\left( 0 \right)} \right\rangle = \frac{1} {{\sqrt 2 }}\left( {\left| {\left. {01} \right\rangle \pm } \right|\left. {10} \right\rangle } \right)} \right., in the absence of spin-orbit interaction D and the inhomogeneity parameter b. Therefore, it is possible to perform quantum teleportation protocol T₀\mathcal{T}_0 and entanglement teleportation T₁\mathcal{T}_1, with perfect quality, by choosing a proper set of parameters and employing one of these maximally entangled robust states as the initial state of the resource.     

Quantum Entanglement Under Lorentz Transformation

We study the properties of quantum entanglement in moving frames, with a non-maximally entangled bipartite state: $|\phi\rangle=\sqrt{1-\varepsilon}|{\uparrow\uparrow}\rangle +\sqrt{\varepsilon}|{\downarrow\downarrow}\rangle$ , (0<ε<1). We calculate the concurrence of this state under Lorentz transformation and show that if the momenta part of the spin-1/2 pair is appropriately correlated, the concurrence is invariant ( $\mathcal {C}(\rho)=2\sqrt{\varepsilon-\varepsilon^{2}}$ ); despite the entanglement of this state is not maximal, there is no transfer of entanglement between spin and momentum.     

Amplitude-squared squeezing in superposed coherent states

We study amplitude-squared squeezing of the Hermitian operator Z_θ=Z₁ cosθ+Z₂ sin θ, in the most general superposition state , of two coherent states and . Here operators Z_1,2 are defined by , a is annihilation operator, θ is angle, and complex numbers C_1,2 , α, β are arbitrary and only restriction on these is the normalization condition of the state . We define the condition for a state to be amplitude-squared squeezed for the operator Z_θ if squeezing parameter , where N=a⁺a and . We find maximum amplitude-squared squeezing of Z_θ in the superposed coherent state with minimum value 0.3268 of the parameter S for an infinite combinations with α- β= 2.16 exp [±i(π/4) + iθ/2], and with arbitrary values of (α+β) and θ. For this minimum value of squeezing parameter S, the expectation value of photon number can vary from the minimum value 1.0481 to infinity. Variations of the parameter S with different variables at maximum amplitude-squared squeezing are also discussed.     

Controlling on Entangled Decoherence by the Interaction Model Between Qubit and Environment

The entangling evolution of the coupled qubits interacting with non-Markov environment is investigated in terms of concurrence. The results show that the entanglement of quantum systems depends on not only the initial state of system but also the coupling ways between qubit and environment. It shows that: (1) when the system is initially in ( | 00 ?±| 11 ?)/?2( | 00 \rangle\pm| 11 \rangle)/\sqrt{2} state or in the mixed state which is produced by the state, if we can control the coupling between the qubits and the environment in a asymmetrical state, we can make the quantum system always in the entangled state. (2) For an initial state ( | 01 ?±| 10 ?)/?2( | 01 \rangle\pm| 10 \rangle)/\sqrt{2} or in its mixed state, in contrast, there will not be entangled death under the symmetric coupling. We also find that, in ( | 01 ?±| 10?)/?2( | 01 \rangle\pm| 10\rangle)/\sqrt{2} or in its mixed state, the stronger the interaction between qubits is, the better to struggle against entanglement sudden death is.     

Unifying the theory of integration within normal-, Weyl- and antinormal-ordering of operators and the s-ordered operator expansion formula of density operators

By introducing the s-parameterized generalized Wigner operator into phase-space quantum mechanics we invent the technique of integration within s-ordered product of operators(which considers normally ordered,antinormally ordered and Weyl ordered product of operators as its special cases).The s-ordered operator expansion(denoted by...) formula of density operators is derived,which is ρ = 2 1 s ∫ d2βπβ|ρ |β exp { 2 s 1(s|β|2 β a + βa a a) }.The s-parameterized quantization scheme is thus completely established.     

Cluster-state preparation in thermal cavities without single-qubit operation

A potential scheme is proposed for generating cluster states of many atoms in cavity quantum electradynamics （QED）, in which an unorthodox encoding is employed with the ground state being qubit [0〉 while two closely spaced upper states being qubit ｜1〉. Throughout the scheme the cavities can be in thermal states but axe only virtually excited. We show how to create the cluster states by performing a two-step hut no single-qubit operation. Discussion is also carried out on the experimental feasibility of our scheme.