Threshold effect for probabilistic entanglement swapping

TL;DR

This paper introduces probabilistic entanglement swapping methods using varied initial entanglement levels and non-Bell measurements, revealing a threshold effect where high measurement entanglement guarantees optimal EPR projection probability.

Contribution

It proposes new probabilistic swapping strategies with a non-Bell basis and demonstrates a threshold effect in measurement entanglement for successful EPR projection.

Findings

A twofold entanglement threshold effect related to measurement basis concurrence.

Maximal measurement entanglement is not necessary for optimal EPR projection.

Four strategies for probabilistic entanglement swapping are designed.

Abstract

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.