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.     

Modulation of Entanglement for Coupled Superconducting Qubits Under Non-Markovian Environment

The evolution of entanglement decoherence is investigated for a coupled superconducting qubit under non-Markovian environment by utilizing a commensal entanglement degree. The results show that, owing to the memory feedback effect of environment, the entanglement degree of the coupled qubits at the thermal equilibrium always monotonously tends to zero so that entanglement sudden death occurs briefly in the non-Markovian process. Different from the Markovian process, stronger the dissipation is, faster the entanglement sudden death is. We find that, furthermore, the interaction between the qubits results generally in reduction of entanglement degree in the quantum system. With some special initial states or initial phase angles, however, the influence of the interaction between qubits on the system entanglement degree can be avoided.     

Optimizing quantum correlation dynamics by weak measurement in dissipative environment

We investigate the protection of quantum correlations of two qubits in independent vacuum reservoirs by means of weak measurements. It is found that the weak measurement can reduce the amount of quantum correlation for one type of initial state at the beginning in a non-Markovian environment and meanwhile it can reduce the occurrence time of entanglement sudden death(ESD) in the process of time evolution. In a Markovian environment, the quantum entanglements of the two kinds of initial states decay rapidly and the weak measurement can further weaken the quantum entanglement,therefore in this case the entanglement cannot be optimized in the evolution process.     

Controlling Sudden Birth and Sudden Death of Entanglement at Finite Temperature

The decoherence and the decay of quantum entanglement due to both population relaxation and thermal effects are investigated for the two qubits initially prepared in the extended Werner-like state by solving the Lindblad form of the master equation, where each qubit is interacting with an independent reservoir at finite temperature T. Entanglement sudden death (ESD) and entanglement sudden birth (ESB) are observed during the evolution process. We analyze in detail the effects of the mixedness, the degree of entanglement of the initial states and finite temperature on the time of entanglement sudden death and entanglement sudden birth. We also obtain an analytic formula for the steady state concurrence that shows its dependence on both the system parameters, the decoherence rate and finite temperature. These results arising from the combination of extended Werner-like initial state and independent thermal reservoirs suggest an approach to control the maximum possible concurrence even after the purity and finite temperature induce sudden birth, death and revival.     

The entanglement dynamics of two coupled qubits in different environment

In this Letter, the entanglement dynamics of two interacting qubits in a common bath and in two independent baths, at finite and zero temperature are investigated. Entanglement sudden death (ESD) and entanglement sudden birth (ESB) are observed when the two qubits are embedded in two independent baths at finite temperature. At zero temperature, the entanglement of the two qubits may evolve to a steady state with non-zero value when the two qubits are embedded in a common bath, the entanglement sudden birth does not occur when the qubits are embedded in two independent baths.     

Entanglement for Two Dissipative Qubits

Entanglement dynamics of two qubits from environmental perturbations with different initial conditions is investigated. The results show that the qubit-qubit interaction leads to a periodic disentanglement and entanglement. It is surprised that the sudden death of entanglement (ESD) does not happen for non-interacting qubits, but for both the cases of a pure dephasing environment and a normal environment, ESD emerges. The results may provide a useful clue to implement an entanglement quantum information.     

Entanglement for Two-Qubit Extended Werner-Like States: Effect of Non-Markovian Environments

We investigate the sudden birth and sudden death of entanglement of two qubits interacting with uncorrelated structured reservoirs. The system is initially prepared in two-qubit extended Werner-like state. We work out the dependence of the entanglement dynamics on both non-Markovian environments and the purity of initial state, and show that non-Markovian environments and the purity can control the time of the two-qubit entanglement sudden death and the reservoirs' entanglement sudden birth.Furthermore, under the conditions of different purity and initial entanglement, the revival of qubits' entanglement can manifest before, simultaneously or even after the disentanglement of their corresponding reservoirs.     

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

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.     

Sudden death and birth of entanglement beyond the Markovian approximation

We investigate the entanglement dynamics of two initially entangled qubits interacting independently with two uncorrelated reservoirs beyond the Markovian approximation. Quite different from the Markovian reservoirs [C.E. López, et al., Phys. Rev. Lett. 101 (2008) 080503], we find that entanglement sudden birth (ESB) of the two reservoirs occurs without certain symmetry with respect to the entanglement sudden death (ESD) of the two qubits. A phenomenological interpretation of entanglement revival is also given.     

Entanglement sudden death in band gaps

Using the pseudomode method, we evaluate exactly time-dependent entanglement for two independent qubits, each coupled to a non-Markovian structured environment. Our results suggest a possible way to retard entanglement sudden death by modifying the qubit-pseudomode detuning and the spectrum of the reservoirs. Particularly, in environments structured by a model of a density-of-states gap which has two poles, entanglement trapping and prevention of entanglement sudden death occur in the weak-coupling regime.     

Influence of Interaction Between Qubits on Entanglement Sudden Death and Birth

Dynamic evolution of entanglement is studied for coupling two-qubit system in non-Markov environment in terms of concurrence. We find that the degree of entanglement depends on the initial quantum state of the system and the interaction between the two-qubit system and the environment. When the interaction between the qubits and the environment is completely symmetric, especially, the environment has no effect on the entanglement, where the decoherence is entirely resulted from the interaction between qubits. By controlling the coupling way of the interaction, thus, one may avoid the entanglement sudden death (ESD).     

Induced entanglement revival and entanglement protection in a two qubit system

A system of two initially entangled qubits interacting with a bosonic environment is considered. The interaction induces a loss of the initial entanglement of the two qubits, and for specific initial states it causes entanglement sudden death. An investigation of the modifications on the entanglement dynamics by a single pulse control field, performed in the two qubit system, shows that the control field can not only protect entangled states against sudden death but also induce a revival of entanglement in the two qubit system.     

Non-Markovian entanglement dynamics in coupled superconducting qubit systems

We theoretically analyze the entanglement generation and dynamics by coupled Josephson junction qubits. Considering a current-biased Josephson junction (CBJJ), we generate maximally entangled states. In particular, the entanglement dynamics is considered as a function of the decoherence parameters, such as the temperature, the ratio r ≡ w_c\omega_c/w₀\omega_0 between the reservoir cutoff frequency w_c\omega_c and the system oscillator frequency w₀\omega_0,
and the energy levels split of the superconducting circuits in the non-Markovian master equation. We analyzed the entanglement sudden death (ESD) and entanglement sudden birth (ESB) by the non-Markovian master equation. Furthermore, we find that the larger the ratio r and the thermal energy k _BT , the shorter the decoherence. In this superconducting qubit system we find that the entanglement can be controlled and the ESD time can be prolonged by adjusting the temperature and the superconducting phases F_k\Phi_k which split the energy levels.     

Entanglement death and teleportation pre-emption in a dissipative system of two coupled qubits

We discuss the entanglement of two coupled qubits each of which is interacting with a multi-mode squeezed vacuum field reservoir and the possibility to use them in a teleportation protocol. The entanglement sudden death (ESD) and teleportation pre-emption (TPE) are discovered in this system. We consider the interplay between the coupling strength and the squeezing parameter, and find that they play competing roles in entanglement as well as in teleportation. We show in detail how the entanglement decay affects the teleportation. It is interesting to show that TPE precedes ESD in general, and for given measurement result and squeeze parameter all output states of teleportation for a long time arrive at a fixed asymptotic point in the Bloch sphere.     

非马尔科夫环境下耦合超导量子系统纠缠演化的数值研究

基于耦合超导量子比特系统模型下,在非马尔科夫环境中利用共生纠缠的方法分析了耦合系统纠缠的产生及其动力学的演化。研究了不同初始纠缠态下的纠缠猝死(ESD)和纠缠再生(ESB)现象;主要分析了系统耦合强度、库的截止频率与系统的振荡频率间的比值、温度和约瑟夫森能级差对纠缠演化的影响。结果表明:系统纠缠取决于初始纠缠态和系统的耦合强度J,并且通过调节以上非马尔科夫环境的相干参数可以延长解纠缠时间来确保量子计算过程中的应用和量子信息的实现。     

Entanglement dynamics of two-bipartite system under the influence of dissipative environments

An experimental scheme is suggested that permits a direct measure of entanglement in a two-qubit cavity system. It is realized in the cavity-QED technology utilizing atoms as flying qubits. With this scheme we generate two different measures of entanglement, namely logarithmic negativity and concurrence. The phenomenon of sudden death entanglement (ESD) in a bipartite system subjected to dissipative environment is examined. We show that the sudden death time of the entangled states depends on the initial preparation of the entangled state and the temperature of the reservoir.     

Classical correlation, quantum discord and entanglement for two-qubit system subject to heat bath

Classical correlation (CC), quantum discord (QD) and entanglement (QE) of two qubits in one-side and two-side decoherence models are investigated. The sudden change of quantum discord (DSC) as well as classical correlation and sudden death of entanglement (ESD) are found. It is proved that QE (QD) presents no sudden change (sudden death). We prove that, for nonzero occupation number of the reservoir, QE must suffer sudden death; For zero occupation number and X-form initial states, we obtain the states which are robust and the states which experience sudden death. It is verified that if DSC and ESD occur under one-side decoherence, then it must appear in the two-side decoherence, while the reverse does not hold. We obtain the boundaries of CC-QE plane and QD-QE plane, and give the state possessing maximal amount of CC (QD) for a given amount of QE.     

Effect of non-Markovianity on synchronization

We investigate the transient spontaneous quantum synchronization between two qubits interacting with a common non-Markovian environment based on a collision model. We are mainly interested in the effect of non-Markovianity on the synchronization between two qubits. We find that the non-Markovianity always delay the anti-synchronization and decrease the parameter region where the qubits get anti-synchronized. Meanwhile, we define V to characterize the visibility of synchronization and show that there is an apparent link among V, entanglement and quantum mutual information whether in the Markovian or non-Markovian regimes when the environment is in the vacuum state. Moreover, with the increase of temperature, the parameter region of the emergence of anti-synchronization and the time to get anti-synchronized in the non-Markovian regime gradually approaches that in the Markovian regime. The high temperature decreases the parameter region of the emergence of anti-synchronization in both Markovian and non-Markovian regimes, and breaks the connection among V, entanglement and quantum mutual information.     

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.     

Control of entanglement sudden death induced by Dzyaloshinskii-Moriya interaction

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,andproperly mixing the initial state of the system and adjusting the state of qubit C are two effective methods of controlling ESD.