# Entanglement and quantum discord in optically coupled coherent Ising machines

## TL;DR

This paper investigates the presence and behavior of entanglement and quantum discord in dissipatively coupled coherent Ising machines, using analytical and numerical methods across different coupling regimes and system sizes.

## Contribution

It provides the first comprehensive analysis of entanglement and quantum discord in CIMs, including analytical solutions and numerical simulations for various coupling strengths and system configurations.

## Key findings

- Entanglement disappears when background loss exceeds Ising coupling.
- Quantum discord remains finite even with large linear loss.
- Entanglement diminishes with distance in a 1D lattice, but discord persists.

## Abstract

We present analytical and numerical simulation results for squeezing, entanglement, and quantum discord in a dissipatively coupled coherent Ising machine (CIM). Both analytical solutions and numerical simulation results, which are obtained with positive-P, truncated-Wigner and truncated-Husimi representations for the density operator, predict the presence of entanglement and quantum discord, below and above the threshold of CIM. The entanglement criteria and quantum discord are evaluated as a function of the dissipative coupling strength relative to the background loss. For coupled two DOPOs, while entanglement disappears as the background loss exceeds the Ising coupling strength, the quantum discord remains finite even with a large linear loss. For one-dimensional lattice of DOPOs, while entanglement disappears for DOPO pair with large distance, quantum discord remains finite.