Entanglement-swapping for X-states demands threshold values

TL;DR

This paper investigates entanglement swapping using X-states, identifying threshold values for input entanglement necessary for nonseparable outcomes and analyzing the distribution of entanglement after the process.

Contribution

It introduces a scheme for entanglement swapping with X-states, deriving threshold conditions and analyzing outcome entanglement distributions, which was not previously explored.

Findings

Two threshold values for input entanglement for nonseparable outcomes.

Outcome entanglement can be greater or less than input entanglement.

Probability of higher outcome entanglement is lower than that of lower outcome.

Abstract

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.