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Journal of the Korean Physical Society

Non-Markovian effects on entanglement swapping

Jin Woo Jun

Published Feb 1, 2012• 2 citations
Publisher

Abstract

We show that, under the influence of non-Markovian environments on the entanglement swapping protocol, the maximally entangled antisymmetric Bell state produces more entanglement between the two final particles than the maximally entangled symmetric Bell state. We elucidate how negativity, concurrence, and geometric discord could account for this behavior.

DOI
10.3938/jkps.60.550

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We show that, under the influence of non-Markovian environments on the entanglement swapping protocol, the maximally entangled antisymmetric Bell state produces more entanglement between the two final particles than the maximally entangled symmetric Bell state. We elucidate how negativity, concurrence, and geometric discord could account for this behavior.
We show how, under the influence of non-Markovian environments, two different maximally entangled Bell states give rise to states that have equal classical correlations and the same capacities to violate the Bell-Clauser-Horne-Shimony-Holt inequality, but intriguingly differing usefulness for teleportation and dense coding. We elucidate how different entanglement measures like negativity and concurrence, and two different measures of quantum discord, could account for these behaviors. In particular, we explicitly show how the Ollivier-Zurek measure of discord directly accounts for one state being a better resource for dense coding compared to another. Our study leads to several important issues about these measures of discord.
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.
The nonlocal correlations between quantum states in an entangled system are essential to many quantum communications applications. A basic quantum operation, which permits the distribution of entanglement between two initially uncorrelated systems, is entanglement swapping. Here we present a rigorous formulation of entanglement swapping of any two partially mixed two-qubit states without limiting ourselves to any specific type of state or noise. Further, for two important classes of the input states, Bell diagonal and pure states, we describe how the concurrence of the final state is related to the concurrence of the initial states. First, we consider Bell diagonal states, and find bounds on the concurrence of the final state in terms of the concurrences of the initial states. These bounds are important for communications applications because polarization mode dispersion in fibers produces Bell diagonal states up to a local unitary rotation. Second, we show that swapping pure states occasionally results in a state of higher concurrence than either of the initial states. In addition, we find that two pure states are most likely to be capable of swapping to a state of increased concurrence when the two initial states have similar concurrences. Our analysis offers a completely general framework for investigating the behavior of any pair of two-qubit states when used for entanglement swapping.
The basic entanglement swapping protocol allows to achieve the main aim of deterministically projecting two qubits, which have never interacted, onto a maximally entangled state. For deterministic swapping the key ingredient is the maximal entanglement initially contained in two pairs of qubits and the ability to measure onto a Bell basis. In other words, the basic and deterministic entanglement swapping scheme involves three maximal level of entanglement. In this work we address probabilistic entanglement swapping processes performed with different amounts of initial entanglement. Besides, we suggest a non Bell measuring-basis, thus we introduce a third entanglement level in the process. Additionally, we propose the \emph{unambiguous state extraction} scheme as the local mechanism for probabilistically achieving the main aim. Amalgamating these three elements allows us to design four strategies for performing probabilistic entanglement swapping. Surprisingly, we encountered an twofold entanglement matching effect related to the concurrence of the measuring-basis. Specifically, the maximal probability of accomplishing the main aim becomes a constant for concurrences higher than or equal to the matching entanglement values. Thus, we show that maximal entanglement in the measuring-basis is not required for attaining the main aim with optimal probability.
We study the evolution of quantum correlations in two-particle discrete-time non-unitary quantum walks on a line with gain and loss. The two particles are initially prepared in a maximally entangled state and evolve independently. Using numerically exact calculations of position probability densities, average interparticle distance, entanglement entropy, and concurrence, we examine how dissipation and particle-exchange symmetry of the state (symmetric or antisymmetric) influence the resulting correlations. Notably, we find that the entanglement entropy of the antisymmetric state decays slower than that of the symmetric state at the exceptional point of the model. We also show that, in the antisymmetric state, the concurrence measured on the one-particle reduced density operator is unaffected by dissipation. Furthermore, we discuss how these correlations indicate quantum-to-classical transitions through the appearance of Gaussian position probability densities, sub-linear growth of average interparticle distance after a few steps, and decay of the entanglement entropy. On the other hand, the robustness of the qubit entanglement entropy can differentiate the model's topological phases better than in the one-particle quantum walk scenario.
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.