Luis Roa

The basic \emph{entanglement swapping protocol} allows to project two qubits, which have never interacted, onto a maximally entangled state. For deterministic swapping, the key ingredient is the maximal entanglement that was initially contained in two pairs of qubits and the capacity of projecting onto a Bell basis. Thus the basic and deterministic entanglement swapping scheme involves three maximal level of entanglement. In this work we propose probabilistic entanglement swapping processes performed with different amounts of initial entanglement. Besides that we suggest a non Bell measuring-basis, to 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 EPR projection. The combination of these three elements allows us to design four strategies for performing probabilistic entanglement swapping. Surprisingly, we find a twofold entanglement threshold effect related to the concurrence of the measuring-basis. Specifically, the maximal probability of accomplishing a EPR projection becomes a constant for concurrences higher than or equal to threshold entanglement value. Thus, we show that maximal entanglement in the measuring-basis is not required for attaining the EPR projection.

In this paper we redesign the probabilistic teleportation scheme considered in Phys. Rev. A61, 034301 (2000) by Wan-Li Li et al., where the optimal state extraction protocol complements the basic teleportation process with a partially entangled pure state channel, in order to transfer the unknown state with fidelity 1. Unlike that scheme, where the information of the unknown state is lost if the state extraction fails, our proposal teleports exactly and optimally an unknown state, and allows to recover faithfully that state when the process has not succeeded. In order to study the resilience of the scheme, we apply it to the teleportation problem through a quantum channel in a mixed state with pure dephasing. We find that a successful process transfers an unfaithful state, namely, the outcome state acquires the decoherence of the channel, but the unknown state is recovered by the sender with fidelity 1 if the teleportation fails. In addition, in this case, the fidelity of the teleported state has quantum features only if the channel has an amount of entanglement different from zero.

We propose a scheme for a deterministic extraction of entanglement by means of a reduction process involving local von Neumann measurements. In an example of a tripartite system, we show that by choosing appropriate measurement bases for a given qubit, one can map an initial three-qubit state into outcome pure bipartite states with the same amount of entanglement of formation. In addition, by optimizing local projective measurements, one can efficiently convert higher-order correlations, contained in a multipartite state, into their lower-order counterparts, and thus significantly enhance the initial (reduced mixed-state) entanglement. We find the analytical expressions for the bounds of the deterministically extracted entanglement and relate them with the initial three-tangle and bipartite (mixed-state) concurrences.

In our work we consider the following problem in the context of teleportation: an unknown pure state has to be teleported and there are two laboratories which can perform the task. One laboratory uses a pure non-maximally entangled channel but has a capability of performing the joint measurement on bases with a constrained degree of entanglement; the other lab makes use of a mixed X -state channel but can perform a joint measurement on bases with higher entanglement degrees. We compare the average teleportation fidelity achieved in both cases, finding that the fidelity achieved with the X -state can surpass the obtained with a pure channel, even though the X -state is less entangled than the latter. We find the conditions under which this effect occurs. Our results evidence that the entanglement of the joint measurement plays a role as important as the entanglement of the channel in order to optimize the teleportation process. We include an example showing that the average fidelity of teleportation obtained with a Werner state channel can be greater than that obtained with a Bell state channel.

In our work we consider the following problem in the context of teleportation: an unknown pure state have to be teleported and there are two laboratories which can perform the task. One laboratory uses a pure non maximally entangled channel but has a capability of performing the joint measurement on bases with a constrained degree of entanglement; the other lab makes use of a mixed X-state channel but can perform a joint measurement on bases with higher entanglement degrees. We compare the average teleportation fidelity achieved in both cases, finding that the fidelity achieved with the X-state can surpass the obtained with a pure channel, even though the X-state is less entangled than the latter. We find the conditions under which this effect occurs. Our results evidence that the entanglement of the joint measurement plays a role as important as the entanglement of the channel in order to optimize the teleportation process. We include an example showing that the average fidelity of teleportation obtained with a Werner state channel can be grater than that obtained with a Bell state channel.

A protocol for transferring an unknown single qubit state has quantum features when the average fidelity of the outcomes is greater than 2/3. We use the probabilistic and unambiguous state extraction scheme as a mechanism to redistribute the fidelity in the outcome of the teleportation when the process is performed with an X-state as a noisy quantum channel. We show that the entanglement of the channel is necessary but not sufficient in order for the total average fidelity f_X to display quantum features, i.e., we find a threshold C_X for the concurrence of the channel. If the mechanism for redistributing fidelity is successfully applied then we find a filtrable outcome with normalized average fidelity f_{X,USE,0} greater than f_X. In addition, we find the threshold concurrence of the channel C_{X,USE,0} in order for the normalized average fidelity to display quantum features. Surprisingly, we find that the threshold concurrence C_{X,USE,0} can be lesser than C_X. Finally, we show that if the mechanism for redistributing fidelity fails then the respective filtrable outcome has average fidelity lesser than 2/3.

The basic entanglement-swapping scheme can be seen as a process which allows to redistribute the Bell states' properties between different pairs of a four qubits system. Achieving the task requires performing a von Neumann measurement, which projects a pair of factorized qubits randomly onto one of the four Bell states. In this work we propose a similar scheme, by performing the same Bell-von Neumann measurement over two local qubits, each one initially being correlated through an X-state with a spatially distant qubit. This process swaps the X-feature without conditions, whereas the input entanglement is partially distributed in the four possible outcome states under certain conditions. Specifically, we obtain two threshold values for the input entanglement in order for the outcome states to be nonseparable. Besides, we find that there are two possible amounts of outcome entanglement, one is greater and the other less than the input entanglement; the probability of obtaining the greatest outcome entanglement is smaller than the probability of achieving the least one. In addition, we illustrate the distribution of the entanglement for some particular and interesting initial X-states.