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.     

Dynamics of Entanglement for a Two-Parameter Class of States in a Qubit-Qutrit System

We investigate the dynamics of entanglement for a two-parameter class of states in a hybrid qubit-qutrit system under the influence of various dissipative channels. Our results show that entanglement sudden death (ESD) is a general phenomenon and it usually takes place in a qubit-qutrit system interacting with various noisy channels, not only the case with dephasing and depolarizing channels observed by others. ESD can only be avoided for some initially entangled states under some particular noisy channels. Moreover, the environment affects the entanglement and the coherence of the system in very different ways.     

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.     

Asymptotic Entanglement Sudden Death in Two Atoms with Dipole–Dipole and Ising Interactions Coupled to a Radiation Field at Non-Zero Detuning

We investigate the time evolution and asymptotic behavior of a system of two two-level atoms (qubits) interacting off-resonance with a single mode radiation field. The two atoms are coupled to each other through dipole–dipole as well as Ising interactions. An exact analytic solution for the system dynamics that spans the entire phase space is provided. We focus on initial states that cause the system to evolve to entanglement sudden death (ESD) between the two atoms. We find that combining the Ising and dipole–dipole interactions is very powerful in controlling the entanglement dynamics and ESD compared with either one of them separately. Their effects on eliminating ESD may add up constructively or destructively depending on the type of Ising interaction (Ferromagnetic or anti-Ferromagnetic), the detuning parameter value, and the initial state of the system. The asymptotic behavior of the ESD is found to depend substantially on the initial state of the system, where ESD can be entirely eliminated by tuning the system parameters except in the case of an initial correlated Bell state. Interestingly, the entanglement, atomic population and quantum correlation between the two atoms and the field synchronize and reach asymptotically quasi-steady dynamic states. Each one of them ends up as a continuous irregular oscillation, where the collapse periods vanish, with a limited amplitude and an approximately constant mean value that depend on the initial state and the system parameters choice. This indicates an asymptotic continuous exchange of energy (and strong quantum correlation) between the atoms and the field takes place, accompanied by diminished ESD for these chosen setups of the system. This system can be realized in spin states of quantum dots or Rydberg atoms in optical cavities, and superconducting or hybrid qubits in linear resonators.     

Entanglement sudden death in qubit-qutrit systems

We demonstrate the existence of entanglement sudden death (ESD), the complete loss of entanglement in finite time, in qubit-qutrit systems. In particular, ESD is shown to occur in such systems initially prepared in a one-parameter class of entangled mixed states and then subjected to local dephasing noise. Together with previous results, this proves the existence of ESD for some states in all quantum systems for which rigorously defined mixed-state entanglement measures have been identified. We conjecture that ESD exists in all quantum systems prepared in appropriate bipartite states.     

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.     

Degree of Entanglement and Violation of Bell Inequality by Two-Spin-1/2 States

Bell inequality is violated by the quantum mechanical predictions made from an entangled state of the composite system. In this paper we examine this inequality and entanglement measures in the construction of the coherent states for two-qubit pure and mixed states. we find a link to some entanglement measures through some new parameters (amplitudes of coherent states). Conditions for maximal entanglement and separability are then established for both pure and mixed states. Finally, we analyze and compare the violation of Bell inequality for a class of mixed states with the degree of
entanglement by applying the formalism of Horodecki et al.     

控制Tavis-Cummings模型中两原子X态的纠缠突然死亡与突然产生

研究了初态为X态时Tavis-Cummings模型中具有偶极相互作用两原子的纠缠演化特性,在演化过程中,同时号码出现了两原子的纠缠突然死亡(ESD)与突然产生(ESB)两种有趣的现象.详细分析了两原子初始态的纯度、偶极相互作用、光场粒子数对这两种现象出现时间的影响,进一步给出了初始为混态时ESB与ESD的转换条件.计算结果表明,上述系统参量对两原子的纠缠演化、ESB与ESD有重要的影响,偶极相互作用会改变纠缠度的振荡周期,使出现ESD的时间间隔减少;随着初始两原子纠缠纯度的增大,纠缠突然产生以及纠缠突然死亡存在的时间缩短,并且可以提高两原子之间的纠缠;对于特殊的初态,产生了纠缠不变性以及固定的两原子纠缠,该定值受两原子初始状态的纯度控制。     

Entanglement and Decoherence of Coupled Superconductor Qubits in Contact with a Common Environment

The sudden death of entanglement is investigated for non-Markovian dynamic process of a pair interacting flux qubits under a thermal bath. The entangling evolution of the coupled qubits interacting with non-Markov environment is investigated in terms of concurrence. The results show that, for initially two-qubit entangled states, the sudden death of entanglement (ESD) always happens in the thermal reservoir, where the appearance of entanglement sudden death strongly depends on the environment. Especially, ESD of the qubits is easier to occur for non-Markovian process than for Markovian one.     

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.     

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.     

Entanglement Dynamics Between Two Atoms Within Different W-like Initial States

We investigate the entanglement dynamics between two atoms which are trapped in an optical cavity with the help of the concurrence and the negativity for two different kinds of normalized W-like initial states. The results show that one of them can suffer the so-called entanglement sudden death (ESD) depending on parameters of the initial state when the optical cavity in the vacuum state, while the other one does not for whatever parameters. However when the initial optical cavity photon number is nonzero, no matter what W-like state as atoms’ initial state, the atoms’ subsystem always undergoes the ESD phenomenon. Meanwhile, by comparing concurrence with negativity, we find that our model gives a concrete example to support the conclusions in the previous reference.     

Entanglement Evolution Between Various Subsystems of Two Three-level Atoms Interacting with a Two-mode Quantized Field in the Presence of Converter Terms

In this paper, we study the interaction between two Λ-type three-level atoms (a typical qutrit-qutrit system) and two coupled modes of a quantized radiation field in the presence of field-field interaction (parametric down conversion) which are simultaneously injected within an optical cavity. Then, by applying an appropriate canonical transformation, the introduced model is reduced to a well-known form of the generalized Jaynes-Cummings model. Under particular initial conditions for atoms (in some possible states) and the fields (in the finite dimensional pair coherent state) which may be prepared, the explicit form of the state vector of the whole system is analytically evaluated. In order to find the degree of entanglement between different parts of subsystems (“atom+atom”-field, “atom+field”-atom and atom-atom) the dynamics of entanglement through different measures, namely, linear entropy and negativity is evaluated. In each case, the effect of various types of initial atomic states on the above measures are numerically analyzed, in detail. It is indicated that the amount of entanglement can be tuned by choosing appropriate initial states of atoms. Particularly, it is shown that the entanglement sudden death (ESD) can be controlled by adjusting the initial state of the atoms.     

Thermal entanglement versus mixture in a spin chain: Generation of maximally entangled mixed states

We study the two-body entanglement and mixture in a three-qubit XXZ spin chain in thermal equilibrium state at temperature T with an external magnetic field B. The effects of the magnetic field, the anisotropy and the temperature on the entanglement and mixture are considered. We show that the ground states in this system are fully characterized and distinguished by both entanglement and mixture. Thermal entanglement versus the mixture of all two-spin states is investigated. All pairwise states provide an upper bound on the entanglement for a fixed mixture, and some part of the boundary reaches the boundary allowed by physics. As a result, maximally entangled mixed states can be generated by controlling magnetic field and temperature. Especially, in the ground state of the whole system, the explicit forms of maximally entangled mixed states are given. The results provide a new way to generate maximally entangled mixed states and control entanglement.     

Entanglement reciprocation using three level atoms in a lambda configuration

We propose a scheme in which entanglement can be transferred from atoms (discrete variables) to entangled states of cavity fields (continuous variables). The cavities play the role of a kind of quantum memory for entanglement, in such a way that it is possible to retrieve it back to the atoms. In our method, two three level atoms in a lambda configuration, previously entangled, are set to interact with single mode cavity fields prepared in coherent states. During the process, one e-bit of entanglement may be deposited in the cavities in an efficient way. We also show that the stored entanglement may be transferred back to flying atoms.     

Generation of Different Classes of Multipartite Entanglement Using Cavity-QED

Using a system of cavity quantum electrodynamics(QED) we present two schemes for multipartite entanglement generation. In the first scheme, a three-level atom is interacting with three cavities successively. In the second one, two three-level atoms are interacted with a coherent optical cavity. These protocols allow us to generate the six classes of tripartite entanglement(GHZ, W, A-B-C, AB-C, C-AB, and B-AC class states) by controling the interaction time between atoms and cavities. Moreover, they allow us to generate entanglement between the cavity fields degrees of freedom(from the first scheme), and a mixed entanglement between the cavity field degrees of freedom and the atomic degrees of freedom.     

Generation and application of a controllable multi-atom entangled state

In this paper, we present a scheme to prepare a set of the multi-atom entangled states by the cavity quantum electrodynamics (QED) technology. The multi-atom entangled states have some particular entanglement properties. For example, the remaining reduced density matrices ρ_{ij} still retain entanglement or disentanglement when any N-2 atoms of the N atoms are traced out, which can be chosen freely according to our need, and the relative entanglement strength of any pair of atoms (measured by the concurrence) can be arbitrarily adjusted. In addition, they may be completely symmetric under the exchange of any two atoms, and perform certain quantum information tasks, such as telecloning, teleportation, secret sharing and so on.     

Comparative analysis of entanglement measures based on monogamy inequality

We evaluate the monogamy inequality for symmetric, non-symmetric pure states of importance in terms of squared concurrence, squared entanglement of formation, squared negativity of partial transpose and compare the corresponding tangles. We show that though concurrence and concurrence tangle are zero for two special classes of mixed entangled states, both negativity tangle and entanglement of formation(EOF) tangle turn out to be non-zero. A comparison of different tangles is carried out in each case and it is shown that while the concurrence tangle captures the genuine multiqubit entanglement in N-qubit pure states with N distinct spinors(containing GHZ and superposition of W-, obverse W states)either negativity tangle or EOF tangle is to be used as a better measure of entanglement in the W-class of states with two distinct spinors and in the special classes of mixed multiqubit states.     

Dynamics of Entanglement in Qubit-Qutrit with x-Component of DM Interaction

In this present paper,we study the entanglement dynamics in qubit A-qutrit B pair under x component of Dzyaloshinshkii-Moriya interaction(D_x)by taking an auxiliary qubit C.Here,we consider an entangled qubit-qutrit pair initially prepared in two parameter qubit-qutrit states and one auxiliary qubit prepared in pure state interacts with the qutrit of the pair through DM interaction.We trace away the auxiliary qubit and calculate the reduced dynamics in qubit A-qutrit B pair to study the influence of the state of auxiliary qubit C and D_x on entanglement.We find that the state(probability amplitude)of auxiliary qubit does not influence the entanglement,only D_x influences the same.The phenomenon of entanglement sudden death(ESD)induced by D_x has also been observed.We also present the affected and unaffected two parameter qubit-qutrit states by D_x.