Effect of weak measurement on entanglement distribution over noisy channels

TL;DR

This paper explores how null-result weak measurements influence the distribution and distillation of various entangled states over noisy channels, revealing benefits for W states but limited effects on others.

Contribution

It demonstrates that NRWM can enhance the distillation of W states and provides insights into local filtering operations for entanglement protection.

Findings

NRWM does not improve bipartite or GHZ state distribution.

NRWM reduces fidelity thresholds for W state distillability.

NRWM increases the efficiency of W state distillation.

Abstract

Being able to implement effective entanglement distribution in noisy environments is a key step towards practical quantum communication, and long-term efforts have been made on the development of it. Recently, it has been found that the null-result weak measurement (NRWM) can be used to enhance probabilistically the entanglement of a single copy of amplitude-damped entangled state. This paper investigates remote distributions of bipartite and multipartite entangled states in the amplitudedamping environment by combining NRWMs and entanglement distillation protocols (EDPs). We show that the NRWM has no positive effect on the distribution of bipartite maximally entangled states and multipartite Greenberger-Horne-Zeilinger states, although it is able to increase the amount of entanglement of each source state (noisy entangled state) of EDPs with a certain probability. However, we find that the NRWM would contribute to remote distributions of multipartite W states. We demonstrate that the NRWM can not only reduce the fidelity thresholds for distillability of decohered W states, but also raise the distillation efficiencies of W states. Our results suggest a new idea for quantifying the ability of a local filtering operation in protecting entanglement from decoherence.