Optimal concentrating arbitrary partially entangled W states with linear optics

TL;DR

This paper introduces two optimal linear optics-based entanglement concentration protocols for arbitrary multi-mode W states, enhancing success probability and preserving entanglement for quantum communication.

Contribution

The paper presents the first linear optics protocols that optimally concentrate arbitrary multi-mode W states without auxiliary photons, achieving success probabilities based on the smallest Schmidt coefficient.

Findings

Success probability equals the Nth power of the smallest Schmidt coefficient.

Concentrated states remain maximally entangled, unlike previous protocols.

Protocols are feasible with current linear optical technology.

Abstract

We propose two optimal entanglement concentration protocols (ECPs) for arbitrary single-photon multi-mode W state and multi-photon polarization W state, respectively. In both ECPs, we only require one pair of partially entangled W state, and do not consume any auxiliary photon. Both ECPs are based on the linear optics which can be easily realized. On the other hand, the concentrated maximally entangled states can be remained, which are quite different from the previous ECPs. Moreover, for the concentration of the arbitrary single-photon N-mode W state or N-mode polarization W state, the total success probability is equal to Nth the modulus square of the Schmidt coefficient of the smallest magnitude. It makes both ECPs optimal than all the previous ECPs. Our ECPs may be useful in current quantum communication fields.