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arXiv:1607.07960 · Physical Review A

Entanglement swapping between dissipative systems

Alireza Nourmandipour, Mohammad Kazem Tavassoly

Published Aug 29, 2016• 20 citations
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Abstract

In this paper, we investigate the possibility of entanglement swapping between two distinct qubits coupled to their own (in general) non-Markovian environments. This goal is achieved by performing Bell state measurement on photons leaving dissipative cavities. In the continuation, we introduce the concept of entangling power to measure the average of swapped entanglement over all possible pure initial states. Then we present our results in two regimes, strong and weak coupling, and discuss the role of the detuning parameter in each regime in the amount of swapped entanglement. We also determine the conditions under which the maximum amount of entanglement can be swapped between the two qubits. It is revealed that, despite the presence of dissipation, it is possible to create long-living stationary entanglement between the two qubits.

DOI
10.1103/physreva.94.022339

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In this paper, we investigate the possibility of entanglement swapping between two distinct qubits coupled to their own (in general) non-Markovian environments. This goal is achieved by performing Bell state measurement on photons leaving dissipative cavities. In the continuation, we introduce the concept of entangling power to measure the average of swapped entanglement over all possible pure initial states. Then we present our results in two regimes, strong and weak coupling, and discuss the role of the detuning parameter in each regime in the amount of swapped entanglement. We also determine the conditions under which the maximum amount of entanglement can be swapped between the two qubits. It is revealed that, despite the presence of dissipation, it is possible to create long-living stationary entanglement between the two qubits.
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.
We provide an analytical investigation of the pairwise entanglement dynamics for a system, consisting of an arbitrary number of qubits dissipating into a common and non-Markovian environment for both weak- and strong-coupling regimes. In the latter case, a revival of pairwise entanglement due to the memory depth of the environment is observed. The leakage of photons into a continuum state is assumed to be the source of dissipation. We show that for an initially Werner state, the environment washes out the pairwise entanglement, but a series of nonselective measurements can protect the relevant entanglement. On the other hand, by limiting the number of qubits initially in the superposition of single excitation, a stationary entanglement can be created between qubits initially in the excited and ground states. Finally, we determine the stationary distribution of the entanglement versus the total number of qubits in the system.
Entanglement swapping is gaining widespread attention due to its application in entanglement distribution among different parts of quantum appliances. We investigate the entanglement swapping for pure and noisy systems, and argue different entanglement quantifiers for quantum states. We explore the relationship between the entanglement of initial states and the average entanglement of final states in terms of concurrence and negativity. We find that if initial quantum states are maximally entangled and we make measurements in the Bell basis, then average concurrence and average negativity of final states give similar results. In this case, we simply obtain the average concurrence (average negativity) of the final states by taking the product of concurrences (negativities) of the initial states. However, the measurement in non-maximally entangled basis during entanglement swapping degrades the average swapped entanglement. Further, the product of the entanglement of the initial mixed states provides an upper bound to the average swapped entanglement of final states obtained after entanglement swapping. The negativity work well for weak entangled noisy states but concurrence gives better results for relatively strong entanglement regimes. We also discuss how successfully the output state can be used as a channel for the teleportation of an unknown qubit.
In this paper, we provide an analytical investigation of the entanglement dynamics of moving qubits dissipating into a common and (in general) non-Markovian environment for both weak and strong coupling regimes. We first consider the case of two moving qubits in a common environment and then generalize it to an arbitrary number of moving qubits. Our results show that when the system evolves from an initial entangled state, the amount of initial entanglement decreases and finally disappears after a finite interval of time due to the environmental effects. Moreover, we observe that the movement of qubits has a constructive role in the protection of the initial entanglement. In a sense, in this case, we observe a Zeno-like effect due to the velocity of qubits. On the other hand, we demonstrate how a stationary state of entanglement may be achieved when we consider the case in which at least one of the moving qubits is initially in the ground state. Surprisingly, we observe that when we extend the number of moving qubits with the same velocity, the stationary state of the qubits does not depend on the velocity of qubits as well as on the environmental properties. This means that, in this condition, the stationary state of entanglement depends only on the number of moving qubits.
In this paper, a scheme for the generation of long-living entanglement between two distant Λ-type three-level atoms separately trapped in two dissipative cavities is proposed. In this scheme, two dissipative cavities are coupled to their own non-Markovian environments and two three-level atoms are driven by the classical fields. The entangled state between the two atoms is produced by performing Bell state measurement (BSM) on photons leaving the dissipative cavities. Using the time-dependent Schördinger equation, we obtain the analytical results for the evolution of the entanglement. It is revealed that, by manipulating the detunings of classical field, the long-living stationary entanglement between two atoms can be generated in the presence of dissipation.
We consider a model of two qubits dissipating into both local and global environments (generally at non-zero temperatures), with the possibility of interpolating between purely local dissipation and purely global one. The corresponding dissipative dynamical map is characterized in terms of its Kraus operators focusing on the stationary regime. We then determine conditions under which entanglement can be induced by the action of such a map. It results (rather counterintuitively) that in order to have entanglement in the presence of local environment, this latter must be at nonzero temperature.