Entanglement concentration protocols for GHZ-type entangled coherent state based on linear optics

TL;DR

This paper introduces two linear optics-based entanglement concentration protocols to convert partially entangled GHZ-type entangled coherent states into maximally entangled states, with higher success probabilities demonstrated for larger state parameters.

Contribution

The paper presents two novel entanglement concentration protocols for GHZ-type ECSs, including detailed optical circuit designs and success probability analysis, advancing experimental feasibility.

Findings

First ECP achieves higher success probability than W-type ECS for larger parameters.

Optical circuits are feasible with current linear optical technology.

Success probabilities are explicitly calculated and compared.

Abstract

We proposed two entanglement concentration protocols (ECPs) to obtain maximally entangled Greenberger-Horne-Zeilinger (GHZ)-type entangled coherent state (ECS) from the corresponding partially entangled GHZ-type ECSs. We obtained the first ECP using a partially entangled GHZ-type ECS assisted with a superposition of single-mode coherent state, however the second ECP is designed using two copies of partially entangled GHZ-type ECSs. The success probabilities have also been calculated and discussed for both the ECPs. We have further compared the success probabilities of our first ECP for 3-mode GHZ-type ECS with an ECP of 3-mode W-type ECS and found that our ECP is more efficient (maximal success probabilities) for larger value (\beta=0.7) of state parameter. For the physical realization, two optical circuits (for two ECPs) using linear optical elements, viz 50:50 beam splitter, phase shifter, and photon detectors are provided, which support the future experimental implementation possible with the present technology.