# Locally optimal symplectic control of multimode Gaussian states

## TL;DR

This paper develops locally optimal quantum control strategies using Gaussian unitaries to accelerate the relaxation of multimode Gaussian states in lossy channels, highlighting the role of squeezing in optimizing entropy and temperature dynamics.

## Contribution

It derives conditions for optimal control of Gaussian states in lossy channels, providing explicit relaxation times and emphasizing the importance of squeezing in the process.

## Key findings

- Squeezing enhances the rate of entropy change during relaxation.
- Exact relaxation times are computed for optimal heating and cooling.
- Control strategies are tailored to the parameters governing entropy and temperature.

## Abstract

The relaxation of a system to a steady state is a central point of interest in many attempts to advance control over the quantum world. In this paper, we consider control through instantaneous Gaussian unitary operations on the ubiquitous lossy channel, and find locally optimal conditions for the cooling and heating of a multimode Gaussian state subject to losses and possibly thermal noise. This is done by isolating the parameters that encode entropy and temperature and by deriving an equation for their evolution. This equation is in such a form that it grants clear insight into how relaxation may be helped by instantaneous quantum control. It is thus shown that squeezing is a crucial element in optimising the rate of change of entropic properties under these channels. Exact relaxation times for heating and cooling are derived, up to an arbitrarily small distance from the fixed point of the lossy channel with locally optimal strategies.