Gaussian Thermal Operations and the Limits of Algorithmic Cooling

TL;DR

This paper characterizes Gaussian thermal operations on quantum states, demonstrating fundamental limits on entropy reduction and algorithmic cooling in quantum thermodynamics involving Gaussian environments.

Contribution

It provides a complete characterization of Gaussian thermal operations and establishes that entropy cannot be reduced below environmental temperature using such operations.

Findings

All Gaussian thermal operations are embeddable in Markovian dynamics.

Necessary and sufficient conditions for state transformations in single-mode systems.

Impossibility of entropy reduction below environmental temperature via Gaussian operations.

Abstract

The study of thermal operations allows one to investigate the ultimate possibilities of quantum states and of nanoscale thermal machines. Whilst fairly general, these results typically do not apply to continuous variable systems and do not take into account that, in many practically relevant settings, system-environment interactions are effectively bilinear. Here we tackle these issues by focusing on Gaussian quantum states and channels. We provide a complete characterisation of the most general Gaussian thermal operation acting on an arbitrary number of bosonic modes, which turn out to be all embeddable in a Markovian dynamics, and derive necessary and sufficient conditions for state transformations under such operations in the single-mode case, encompassing states with nonzero coherence in the energy eigenbasis (i.e., squeezed states). Our analysis leads to a no-go result for the technologically relevant task of algorithmic cooling: We show that it is impossible to reduce the entropy of a system coupled to a Gaussian environment below its own or the environmental temperature, by means of a sequence of Gaussian thermal operations interspersed by arbitrary (even non-Gaussian) unitaries. These findings establish fundamental constraints on the usefulness of Gaussian resources for quantum thermodynamic processes.