# Stationary quantum correlations in a system with mean-field PT symmetry

## TL;DR

This paper investigates quantum correlations in a PT-symmetric system of coupled oscillators, revealing persistent quantum correlations without entanglement that are stable under certain gain-loss conditions, using a full quantum noise-inclusive model.

## Contribution

It provides a full quantum analysis of PT-symmetric oscillators, showing quantum correlations can be generated and remain stable beyond classical stability regions.

## Key findings

- Quantum correlations appear without entanglement in the system.
- Quantum correlations become stable above a certain loss threshold.
- Quantum correlations decay in the exact phase but are stable in the broken phase.

## Abstract

A pair of coupled quantum harmonic oscillators, one subject to a gain one to a loss, is a paradigmatic setup to implement PT-symmetric, non-Hermitian Hamiltonians in that one such Hamiltonian governs the mean-field dynamics for equal gain and loss strengths. Through a full quantum description (so as to account for quantum noise) here is shown that when the system starts in any two-mode coherent state, including vacuum, there appear quantum correlations (QCs) without entanglement, as measured by the Gaussian discord. When the loss rate is above a threshold, once generated QCs no more decay. This occurs in a wide region of parameters, significantly larger than that where the full quantum dynamics is stable. For equal gain and loss rates, in particular, QCs decay in the exact phase (including the exceptional point) and are stable in the broken phase.