# Generation of Coherence via Gaussian Measurements

## TL;DR

This paper explores how Gaussian measurements on Gaussian states can generate and enhance quantum coherence in continuous variable systems, both remotely via bipartite correlations and through environmental monitoring.

## Contribution

It introduces methods for remote coherence generation using Gaussian measurements and analyzes coherence dynamics in continuously monitored systems.

## Key findings

- Homodyne detection maximizes remote coherence.
- Threshold coherence distinguishes entangled from separable states.
- Continuous monitoring can increase system coherence.

## Abstract

We address measurement-based generation of quantum coherence in continuous variable systems. We consider Gaussian measurements performed on Gaussian states and focus on two scenarios. In the first one, we assume an initially correlated bipartite state shared by two parties and study how correlations may be exploited to remotely create quantum coherence via measurement back-action. In particular, we focus on conditional states with zero first moments, so as to address coherence due to properties of the covariance matrix. We consider different classes of bipartite states with incoherent marginals and show that the larger the measurement squeezing, the larger the conditional coherence. Homodyne detection is thus the optimal Gaussian measurement to remotely generate coherence. We also show that for squeezed thermal states there exists a threshold value for the generated coherence which separates entangled and separable states at a fixed energy. Finally, we briefly discuss the tripartite case and the relationship between tripartite correlations and the conditional two-mode coherence. In the second scenario, we address the steady state coherence of a system interacting with an environment which is continuously monitored. In particular, we discuss the dynamics of an optical parametric oscillator in order to investigate how the coherence of a Gaussian state may be increased by means of time-continuous Gaussian measurement on the interacting environment.