Quantum Correlations in the Kerr Ising Model

TL;DR

This paper provides a comprehensive quantum mechanical analysis of the Kerr Ising model, revealing non-classical eigenstates and demonstrating a quantum advantage over classical counterparts in specific scenarios.

Contribution

It introduces a full quantum description of the Kerr Ising model, including dissipation and measurement, highlighting non-classical states and quantum advantages.

Findings

Eigenstates are highly non-classical and cat-like.

The energy spectrum is mainly determined by the adjacency matrix.

Quantum advantage observed in anti-ferromagnetic cavity example.

Abstract

In this article we present a full description of the quantum Kerr Ising model---a linear optical network of parametrically pumped Kerr non-linearities. We consider the non-dissapative Kerr Ising model and, using variational techniques, show that the energy spectrum is primarily determined by the adjacency matrix in the Ising model and exhibits highly non-classical cat like eigenstates. We then introduce dissipation to give a quantum mechanical treatment of the measurement process based on homodyne detection via the conditional stochastic Schrodinger equation. Finally we identify a quantum advantage in comparison to the classical analogue for the example of two anti-ferromagnetic cavities.