Dynamics of genuine multipartite entanglement under local non-Markovian dephasing

We study dynamics of genuine entanglement for quantum states of three and four qubits under non-Markovian dephasing. Using a computable entanglement monotone for multipartite systems, we find that the GHZ state is quite resilient state whereas the W state is the most fragile. We compare dynamics of chosen quantum states with dynamics of random pure states and weighted graph states.     

Influence of Composite Effect from Quantum Channels on Entanglement

The dynamics of entanglement between two qubits in the local damping two-sided channel and singlesided channel are compared through non-Markovian process and Markovian process. The entanglement between two qubits is found to be longer in the single-sided channel case due to the weakening of the dissipative effects. In the two-sided channel, influenced by the entanglement between qubits, the previous independent dissipative channels incline to the composite effect of the Markovian process. This composite effect results in the dissipative effect of one channel affecting the qubits in the other channel, especially inhibiting the backflow effect in the non-Markovian channel, which is disadvantageous to the entanglement maintenance between qubits. In the Markovian channel, the composite effect of the damping two-sided channels is more obvious since there is no backflow effect, thus more disadvantageous to the entanglement maintenance.     

Influence of Composite Effect from Quantum Channels on Entanglement

The dynamics of entanglement between two qubits in the local damping two-sided channel and single-sided channel are compared through non-Markovian process and Markovian process. The entanglement between two qubits is found to be longer in the single-sided channel case due to the weakening of the dissipative effects. In the two-sided channel, influenced by the entanglement between qubits, the previous independent dissipative channels incline to the composite effect of the Markovian process. This composite effect results in the dissipative effect of one channel affecting the qubits in the other channel, especially inhibiting the backflow effect in the non-Markovian channel, which is disadvantageous to the entanglement maintenance between qubits. In the Markovian channel, the composite effect of the damping two-sided channels is more obvious since there is no backflow effect, thus more disadvantageous to the entanglement maintenance.     

Boundary states for entanglement robustness under dephasing and bit flip channels

We investigate the robustness of entanglement for a multiqubit system under dephasing and bit flip channels. We exhibit the difference between the entanglement evolution of the two forms of special states, which are locally unitarily equivalent to each other and therefore possess precisely the same entanglement properties, and demonstrate that the difference increases with the number of qubits n. Moreover, those two forms of states are either the most robust genuine entangled states or the most fragile ones, which confirm that local unitary(LU) operations can greatly enhance the entanglement robustness of n-qubit states.     

Entanglement Dynamics of Two Qubits Coupled to a Noise Environment

We study the time evolution of two two-state systems （two qubits） initially in the pure entangled states or the maximally entangled mixed states interacting with the individual environmental noise. It is shown that due to environment noise, all quantum entangled states are very fragile and become a classical mixed state in a short-time limit. But the environment can affect entanglement in very different ways. The type of decoherence process for certain entangled states belongs to amplitude damping, while the others belong to dephasing decoherenee.     

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.     

Quantifying Quantumness with Sudden Birth or Death of Entanglement for Two-Qubits System

Quantumness of the correlations between two qubits, coupled to a cavity field whenever the system is open or closed, is investigated when sudden death (or birth) of the entanglement occurs. It is found that quantum correlation not exists only in the entangled state. It’s found that the dephasing parameters and the purity of the initial states play an important role in the dynamics behaviors of the quantum correlations, including entanglement. Quantumness of the correlations and entanglement, due to dephasing of the cavity, are damped until the same their values which are contained in their initial states.     

Effect of Different Environments on Multipartite Global Discord

We investigate the influences of non-Markovian dissipation and global dephasing process on the dynamical behaviors of global discord among four qubits.We find that for the non-Markovian dissipation model W state is the most robust to decoherence compared to Dicke and GHZ states;however,for the global dephasing model Dicke state is the most robust to decoherence among them.Also the dynamical behaviors of global quantum discord are quite different from that of the multipartite entanglement for the non-Markovian dissipation model,while they are very similar to each other for the global dephasing model.     

Robust and fragile Werner states in the collective dephasing

We investigate the concurrence and Bell violation of the standard Werner state or Werner-like states in the presence of collective dephasing. It is shown that the standard Werner state and certain kinds of Werner-like states are robust against the collective dephasing, and some kinds of Werner-like states is fragile and becomes completely disentangled in a finite-time. The threshold time of complete disentanglement of the fragile Werner-like states is given. The influence of external driving field on the finite-time disentanglement of the standard Werner state or Werner-like states is discussed. Furthermore, we present a simple method to control the stationary state entanglement and Bell violation of two qubits. Finally, we show that the theoretical calculations of fidelity based on the initial Werner state assumption well agree with previous experimental results.     

Thermal and phase decoherence effects on entanglement dynamics of the quantum spin systems

Entanglement dynamics of the N-qubit XY model in thermal and dephasing environments are investigated by solving the Lindblad form of the master equation. Analytical solutions for the two-qubit case and numerical solutions for the multi-qubit case are obtained. For the two-qubit case, our results revealed two main features for entanglement evolution from different initial states. First, the thermal reservoir always induces degradation of the entanglement, and the entanglement may undergo sudden death during certain intervals of the evolution time. Second, the dephasing environment induces damped oscillation of the entanglement for initially separable states and mixed states with relative large values of Δ or J; however, it always induces exponentially decay of the entanglement for the initial Bell states. For the multi-qubit case, our results show that the entanglement decreases monotonically as the time evolves for the initial W state, and behaves as damped oscillation for the initial “one-particle” state. Particularly, for system with large number of qubits, the curves of the concurrence C₁₂ with different N are almost overlapped in dephasing environment.     

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.     

Qubit movement-assisted entanglement swapping

We propose a scheme to generate entanglement between two distant qubits(two-level atom) which are separately trapped in their own(in general) non-Markovian dissipative cavities by utilizing entangling swapping, considering the case in which the qubits can move along their cavity axes rather than a static state of motion. We first examine the role of movement of the qubit by studying the entropy evolution for each subsystem. The average entropy over the initial states of the qubit is calculated. Then by performing a Bell state measurement on the fields leaving the cavities, we swap the entanglement between qubit-field in each cavity into qubit-qubit and field-field subsystems. The entangling power is used to measure the average amount of swapped entanglement over all possible pure initial states. Our results are presented in two weak and strong coupling regimes, illustrating the positive role of movement of the qubits on the swapped entanglement.It is revealed that by considering certain conditions for the initial state of qubits, it is possible to achieve a maximally long-leaving stationary entanglement(Bell state) which is entirely independent of the environmental variables as well as the velocity of qubits. This happens when the two qubits have the same velocities.     

Entanglement of Non-symmetric Two Atomic Qubits Induced by a Coherent State Field

The entanglement of two atomic qubits, which are coupled to a coherent state field with different couplings, is studied. The dynamical evolution of the concurrence, which measures the degree of the entanglement between the two qubits, is plotted versus the scaled time gt. It is found that the two qubits can be entangled by the coherent state field even when they are initially prepared in the most mixed state, and for very weak field, the most mixed state can be more easily entangled than some pure states. It is also found that the entanglement between the qubits sensitively depends on the relative difference of the atomic couplings and the mean photon number of the field.     

Decoherence of interacting qubits in contact with a common environment

Decoherence of interacting two qubits placed under the influence of a common environment is studied by means of the quantum master equation, where the two qubits interact with each other via the XY-coupling and the two-qubit system has the dephasing coupling with the environment. It is shown that when the asymmetry of the interaction between the two-qubit system and environment is not small, the qubit-qubit interaction significantly affects the dephasing of the two-qubit system. To examine such an interaction effect, the decay of two-qubit entanglement is calculated. It is found that the qubit-qubit interaction makes not only the decay of entanglement small but also the period of the oscillatory behaviour short.     

Bound entanglement provides convertibility of pure entangled states

I show that two distant parties can transform pure entangled states to arbitrary pure states by stochastic local operations and classical communication (SLOCC) at the single copy level, if they share bound entangled states. This is the effect of bound entanglement since this entanglement processing is impossible by SLOCC alone. A similar effect of bound entanglement exists in three qubits where two incomparable entangled states of GHZ (Greenberger, Horne, and Zeilinger) and W can be interconverted. In general, multipartite settings composed by N distant parties, all N-partite pure entangled states are interconvertible by SLOCC with the assistance of bound entangled states with positive partial transpose.     

Generation of Entanglement Between Two Noninteracting Qubits via Interaction with Nonclassical Radiation Field

We study the interaction between a single-mode quantized field and a quantum system composed of two qubits. We suppose that two qubits initially be prepared in the mixed and separable state, and study how entanglement between two qubits arises in the course of evolution according to the Jaynes-Cummings type interaction with nonclassical radiation field. We also investigate the relation between entanglement and purity of qubit subsystem. We show that different photon statistics have different effects on the dynamical behavior of the qubit subsystem. When the qubits are initially prepared in the maximally mixed and separable state, for coherent state field we cannot find entanglement between two qubits; for squeezed state field entanglement between two qubits exists in several short period of time; for even and odd coherent state fields of large photon number, the dynamical behavior of the entanglement between two qubits shows collapse and revival phenomenon. For odd coherent state field of small photon number, the entanglement with both qubits initially prepared in maximally mixed state can be stronger than that with both qubits initially prepared in pure states. For fields of small photon number, the entanglement strongly depends on the states they are initially prepared in. For coherent state field, and odd and even coherent state fields of large photon number, the entanglement only depends on the purity of the initial state of qubit subsystem. We also show that during the evolution the unentangled state may be purer than the entangled state, and the maximum degree of entanglement may not occur at the time when the qubit subsystem is in the purist state.     

Generation of Entanglement Between Two Noninteracting Qubits via Interaction with Nonclassical Radiation Field

We study the interaction between a single-mode quantized field and a quantum system composed of two qubits. We suppose that two qubits initially be prepared in the mixed and separable state, and study how entanglement between two qubits arises in the course of evolution according to the Jaynes-Cummings type interaction with nonclassical radiation field. We also investigate the relation between entanglement and purity of qubit subsystem. We show that different photon statistics have different effects on the dynamical behavior of the qubit subsystem. When the qubits are initially prepared in the maximally mixed and separable state, for coherent state field we cannot find entanglement between two qubits; for squeezed state field entanglement between two qubits exists in several short period of time; for even and odd coherent state fields of large photon number, the dynamical behavior of the entanglement between two qubits shows collapse and revival phenomenon. For odd coherent state field of small photon number, the entanglement with both qubits initially prepared in maximally mixed state can be stronger than that with both qubits initially prepared in pure states. For fields of small photon number, the entanglement strongly depends on the states they are initially prepared in. For coherent state field, and odd and even coherent state fields of large photon number, the entanglement only depends on the purity of the initial state of qubit subsystem. We also show that during the evolution the unentangled state may be purer than the entangled state, and the maximum degree of entanglement may not occur at the time when the qubit subsystem is in the purist state.     

Entanglement in four qubit states: Polynomial invariant of degree 2, genuine multipartite concurrence and one-tangle

Characterization of the multipartite mixed state entanglement is still a challenging problem. This is due to the fact that the entanglement for the mixed states, in general, is defined by a convex-roof extension. That is the entanglement measure of a mixed state ρ of a quantum system can be defined as the minimum average entanglement of an ensemble of pure states. In this paper, we show that polynomial entanglement measures of degree 2 of even-N qubits X states is in the full agreement with the genuine multipartite (GM) concurrence. Then, we plot the hierarchy of entanglement classification for four qubit pure states and then using new invariants, we classify the four qubit pure states. We focus on the convex combination of the classes whose at most the one of the invariants is non-zero and find the relationship between entanglement measures consist of non-zero-invariant, GM concurrence and one-tangle. We show that in many entanglement classes of four qubit states, GM concurrence is equal to the square root of one-tangle.     

Entanglement swapping between electromagnetic field modes and matter qubits

Scalable quantum networks require the capability to create, store and distribute entanglement among distant nodes (atoms, trapped ions, charge and spin qubits built on quantum dots, etc.) by means of photonic channels. We show how the entanglement between qubits and electromagnetic field modes allows generation of entangled states of remotely located qubits. We present analytical calculations of linear entropy and the density matrix for the entangled qubits for the system described by the Jaynes-Cummings model. We also discuss the influence of decoherence. The presented scheme is able to drive an initially separable state of two qubits into an highly entangled state suitable for quantum information processing.     

Monogamy and entanglement in tripartite quantum states

We present an interesting monogamy equation for (2⊗2⊗n)-dimensional pure states, by which a quantity is found to characterize the tripartite entanglement with the GHZ type and W type entanglements as a whole. In particular, we, for the first time, reveals that for any quantum state of a pair of qubits, the difference between the two remarkable entanglement measures, concurrence and negativity, characterizes the W type entanglement of tripartite pure states with the two-qubit state as reduced density.