Entanglement swapping and swapped entanglement

TL;DR

This paper analyzes entanglement swapping for pure and noisy quantum systems, examining how initial entanglement and measurement basis affect the entanglement of final states and their utility for quantum teleportation.

Contribution

It investigates the relationship between initial and final entanglement measures, providing bounds and effects of measurement basis on swapped entanglement in quantum systems.

Findings

Maximally entangled initial states with Bell basis measurements yield similar average concurrence and negativity.

Non-maximally entangled measurements degrade the average swapped entanglement.

Product of initial state entanglements bounds the average entanglement of final states.

Abstract

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 average concurrence of finally obtained states provides an upper bound to the average negativity of these states. We also discuss how successfully the output state can be used as a channel for the teleportation of an unknown qubit.