Exponentially Enhanced Scheme for the Heralded Qudit GHZ State in Linear Optics

TL;DR

This paper introduces a highly efficient linear optical scheme for generating high-dimensional multipartite GHZ states with minimal photon resources and improved success probability, advancing quantum information processing capabilities.

Contribution

It presents a novel, resource-efficient linear optical heralded scheme for creating high-dimensional GHZ states with minimal photons and enhanced success rates.

Findings

Requires only $dN$ photons, the minimal number needed.

Achieves substantially higher success probability than previous methods.

Uses linear optical logic gates compatible with various qudit encodings.

Abstract

High-dimensional multipartite entanglement plays a crucial role in quantum information science. However, existing schemes for generating such entanglement become complex and costly as the dimension of quantum units increases. In this work, we overcome the limitation by proposing a significantly enhanced linear optical heralded scheme that generates the $d$-level $N$-partite GHZ state with single-photon sources and linear operations. Our scheme requires $dN$ photons, which is the minimal required photon number, with substantially improved success probability from previous schemes. It employs linear optical logic gates compatible with any qudit encoding system and can generate generalized GHZ states with installments of beamsplitters. With efficient generations of high-dimensional resource states, our work opens avenues for further exploration in high-dimensional quantum information processing.