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 characterization 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.
Highlights
We provide a complete characterization 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
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 unitaries
Introduction and summary.—The past few years have witnessed a resurgence of studies into the thermodynamics of quantum systems [1], which have lent novel insight into the nature of thermodynamic relations, as well as into the role of thermodynamic quantities such as temperature, entropy and work [2,3], set against the practical backdrop of realizing superior thermal machines operating in the quantum regime [4]
Summary
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, systemenvironment interactions are effectively bilinear. It is desirable to single out and characterize subclasses of thermal operations with direct practical relevance To this aim, this Letter shall consider the subclass of Gaussian thermal operations (GTOs), i.e., the class of operations on continuous variable systems obtained by considering energy-preserving bilinear interaction Hamiltonians between the system and a thermal environment. Further specific notation will prove convenient: we shall adopt the shorthand notation S1⁄2σ 1⁄4 SσST and the symbol Trb to denote partial tracing of the bath’s degrees of freedom in the phase space, which just corresponds to pinching out the relevant part of a CM, discarding the rest
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