Entanglement Dynamics of Three Qubits in the Non-Markovian Environments

We consider the entanglement dynamics of three two-level atoms interacting with independent structured non-Markovian reservoirs. The atoms are initially prepared in a mixed multipartite Greenberger—Horne—Zeilinger （GHZ）-type state. Based on the purity and non-Markovian reservoirs, we show that the reservoirs＇ entanglement can exhibit not only multipartite entanglement sudden birth but also entanglement sudden death, and the revival of atom entanglement is not always accompanied by the disentanglement of reservoirs. Meanwhile, we derive the quantitative criteria for multipartite revival and death phenomena and find multipartite entanglement sudden death and entanglement sudden birth simultaneous apparition time is independent of the initial three-qubit state.     

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.     

Effects of Purity on Dynamics of Multipartite Entanglement

We study the effects of purity on entanglement dynamics of a multipartite system in cavity QED. Three two-level atoms A, B and C are initially prepared in an entangled state and locally coupled with independent cavities a, b and c, respectively. We consider the effects of purity of atomic initial state on the entanglement evolution of both the systems of atoms and cavities. It is found that depending on the purity of atomic initial state, the entanglement of atoms （cavities） may or may not exhibit the sudden death （birth） phenomenon.     

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.     

Dzyaloshinskii-Moriya相互作用诱导纠缠突然死亡的控制

We investigate the entanglement dynamics of a system composed of two non-interacting qubits, A and B. A third qubit, C, only has the Dzyaloshinskii-Moriya （DM） spin-orbit interaction with qubit B. We find that the DM interaction can induce the entanglement sudden death （ESD） of the system qubits A and B, and properly mixing the initial state of the system and adjusting the state of qubit C are two effective methods of controlling ESD.     

Entanglement evolution of three-qubit mixed states in multipartite cavity—reservoir systems

We analyze the multipartite entanglement evolution of three-qubit mixed states composed of a GHZ state and a W state.For a composite system consisting of three cavities interacting with independent reservoirs,it is shown that the entanglement evolution is restricted by a set of monogamy relations.Furthermore,as quantified by the negativity,the entanglement dynamical property of the mixed entangled state of cavity photons is investigated.It is found that the three cavity photons can exhibit the phenomenon of entanglement sudden death(ESD).However,compared with the evolution of a generalized three-qubit GHZ state which has the equal initial entanglement,the ESD time of mixed states is later than that of the pure state.Finally,we discuss the entanglement distribution in the multipartite system,and point out the intrinsic relation between the ESD of cavity photons and the entanglement sudden birth of reservoirs.     

Relation between initial conditions and entanglement sudden death for two-qubit extended Werner-like states

In this paper, the dynamical behavior of entanglement of an uncoupled two-qubit system, which interacts with inde- pendent identical amplitude damping environments and is initially prepared in the extended Werner-like （EWL） states, is investigated. The results show that whether entanglement sudden death （ESD） of an EWL state will occur or not depends on initial purity and concurrence. The boundaries between ESD states and ESD-free states for two kinds of EWL states are found to be different. Furthermore, some regions are shown where ESD states can be transformed into ESD-free states by local unitary operations.     

Entanglement and decoherence of coupled superconductor qubits in a non-Markovian environment

The sudden death of entanglement is investigated for the non-Markovian dynamic process of a pair of interacting flux qubits under a thermal bath. The results show that, for initially two-qubit entangled states, entanglement sudden death (ESD) always happens in the thermal reservoir, where its appearance strongly depends on the environment. In particular, ESD of the qubits occurs more easily for the non-Markovian process than for the Markovian one.     

Non-Markovian dynamics of two non-coupled qubits interacting with two separate reservoirs with different spectral densities

The dynamics of two non-coupled qubits independently interacting with their reservoirs is solved by the time convolutionless projection operator method. We study two-qubit quantum correlation dynamics for two different types of spectral densities, which are a Lorentzian distribution and an Ohmic spectral density with a Lorentzian-Drude cutoff function. For two qubits initially prepared in the initial Bell state, quantum discord can keep longer time and reach larger values in nonMarkovian reservoirs for the first spectral distribution or by reducing the cutoff frequency for the second case. For the initial Bell-like state, the dynamic behaviors of quantum discord and entanglement are compared. The results show that a long time of quantum correlation can be obtained by adjusting some parameters in experiment and further confirm that the discord can capture quantum correlation in addition to entanglement.     

Protecting entanglement by detuning: in Markovian environments vs in non-Markovian environments

The models of two qubits separately trapped in two independent Markovian or non-Markovian environments have been investigated. The distinction of the two-qubit entanglement dynamics in different environments has also been discussed in detail. The results show that, in non-Markovian environments, the possible usage time of entanglement can be extended due to its memory effect. On the other hand, we note that, compared to Markovian environments, the two-qubit entanglement could be protected better in non-Markovian environments by modulating the detuning between qubits and cavities. Finally, an intuitive physical interpretation for these results is given.     

Quantum Discord Dynamics of Three Qubits in Non-Markovian Environments

We investigate the dynamics of palrwise quantum discord （QD） for a mixed three-qubit W-type state in three independent non-Markovian reservoirs at zero temperature, each of which is modeled by a leaky cavity with Lorentzian spectral density. The influence of the environment＇s amount of non-Markovianity, the detuning between the qubit frequency and the cavity centre frequency, and the purity of the initial state on the QD dynamics are analyzed in detail. It is found that in the non-Maxkovian regime the system-reservoir interactions induce QD revivals and oscillations no matter whether the detuning is zero or not. Moreover, QD can be preserved for a long time if the non-Markovian condition and the detuning condition are satisfied simultaneously.     

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.     

Bipartite Entanglement Dynamics in Three Qubits System with Dzyaloshinskii-Moriya Interaction

We investigate the bipartite entanglement dynamics of the system composed by three qubits A, B, and C. There is no interaction between A and B, and that of C and B is Dzyaloshinskii-Moriya （DM） spin-orbit interaction. We find that the purity of qubits A and B and the initial state of the qubit C are the two effective parameters to control the entanglement dynamics of the bipartite subsystems. This study sheds some lights on the control of quantum entanglement, which would be helpful for quantum information processing.     

Non-Markovian Effects on Entanglement Dynamics of Three Qubits

We investigate entanglement dynamics of three independent qubits each locally interacting with a zerotemperature non-Markovian reservoir. The effects of environment＇s amount of non-Markovianity or parameters in initial states on the three-qubit entanglement dynamics are presented in detail. It is found that the entanglement of such a system revives after a finite dark period when a proper degree of non-Markovian is present. A deep comparison to that in two-qubit system is also made.     

Sudden death of entanglement of a quantum model

In this paper the so-called sudden death effect of entanglement is investigated in a quantum model. The results show that one can expect the resurrection of the original entanglement to occur in a periodic way following each sudden death event. The length of the time interval for the zero entanglement depends not only on the degree of entanglement of the initial state but also on the initial state.     

Entanglement dynamics of W-like states in an open system

<正>The pairwise entanglement dynamics in a multipartite open system consisting of three entangled cavity photons locally coupled with independent N-mode reservoirs is studied via concurrence.The initial states of cavity photons are prepared in two types of W-like states while the corresponding reservoirs are prepared in the factorable vacuum state.The result shows that all the pairwise concurrences of the total system including cavities and reservoirs undergo qualitatively different dynamical behaviors.Among the two W-like states,only one could exhibit entanglement sudden death(ESD) leading the corresponding reservoirs to exhibit entanglement sudden birth.In addition,by taking the entanglement of the corresponding reservoirs into account,entanglement invariants are constructed for the W-like state that does not undergo ESD.     

Entanglement evolution and transfer in a double Tavis--Cumming model in cavity QED

We have studied entanglement evolution and transfer in a double Tavis--Cumming model where two pairs of entangled two-level atoms AB and CD interact with two single-mode cavity fields a and b. We show that the Bell-like initial state of atoms AB can exhibit entanglement sudden death which should be independent of the initial entanglement of atoms CD. Also, we show that the initial entanglement of one atomic pair can be transferred into another pair, as well as the possible subsystems, that become entangled during evolution.     

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.     

Entanglement dynamics of two distant atoms in two detuning cavities

We investigate the entanglement dynamics via the concurrence of two distant atoms interacting off-resonantly with two cavity fields in Fock states,respectively.We find that the evolution of entanglement has sudden death and sudden birth phenomena,that with the increase of photon numbers in the two cavities,the alternate frequency of sudden death and sudden birth turns fast,and that the amplitude of concurrence oscillates regularly with oscillation frequency becoming slow when the cavity fields have the same photon numbers.While,the maximum of concurrence declines and the amplitude of concurrence oscillates irregularly when the two cavity fields have different photon numbers.In addition,we find the length of death time is dependent on the initial entanglement.     

Sudden death and revival qubits coupled collectively of entanglement of two to a thermal reservoir

In this paper, we investigate the entanglement of two qubits coupled collectively to a common thermal environment and find that the the collective decay can lead to a revival of the entanglement that has already been destroyed. We also show that the ability of the system to revival entanglement relies on the mean photon number of the thermal environment and the degree of entanglement of the initial state.