Passivity and practical work extraction using Gaussian operations

TL;DR

This paper explores the concept of Gaussian passivity in quantum thermodynamics, providing criteria for states resistant to energy lowering via Gaussian unitaries and highlighting the limitations of practical work extraction.

Contribution

It introduces necessary and sufficient conditions for Gaussian passivity and compares it to general passivity, revealing maximal gaps under entropy constraints.

Findings

Gaussian passivity criteria are established.

Maximal energy extraction gap identified.

Gaussian-passive states can still have significant extractable energy.

Abstract

Quantum states that can yield work in a cyclical Hamiltonian process form one of the primary resources in the context of quantum thermodynamics. Conversely, states whose average energy cannot be lowered by unitary transformations are called passive. However, while work may be extracted from non-passive states using arbitrary unitaries, the latter may be hard to realize in practice. It is therefore pertinent to consider the passivity of states under restricted classes of operations that can be feasibly implemented. Here, we ask how restrictive the class of Gaussian unitaries is for the task of work extraction. We investigate the notion of Gaussian passivity, that is, we present necessary and sufficient criteria identifying all states whose energy cannot be lowered by Gaussian unitaries. For all other states we give a prescription for the Gaussian operations that extract the maximal amount of energy. Finally, we show that the gap between passivity and Gaussian passivity is maximal, i.e., Gaussian-passive states may still have a maximal amount of energy that is extractable by arbitrary unitaries, even under entropy constraints.