Passivity and practical work extraction using Gaussian operations

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.

A quantum Otto engine with finite heat baths: energy, correlations, and degradation

“…An important insight into the process of the engine's degradation is gained by looking at the bath-bath correlations instead. Indeed, given that the WM acts as a carrier of both energy and correlations between the baths, and that the baths gradually evolve away from their initial states, one would expect that, over time, the baths get more and more correlated and end up reaching a global passive state (see [57] for the characterization of passivity within GQM). We explore this intuition in figure 7, in which we show that, surprisingly, the mutual information between the two baths remains close to zero during the ideal cycles, and starts abruptly increasing after the last ideal cycle is complete.…”

Concepts of work in autonomous quantum heat engines

“…This ambiguity may perhaps be unsatisfying but we should keep in mind that the term "work" itself carries an inherent operational definition: Work is the "useful" energy transfer to the piston which an agent can afterwards use to perform a task and the remainder is "heat" in the sense of wasted energy. Consider, for example, an agent that is limited to a certain set of unitaries [35] which is incompatible with the piston state generated by the engine-the engine would only produce waste energy ("heat") that cannot be exploited by this agent. A prime example is the Poissonian maser state which cannot be fully exploited with Gaussian operations.…”

“…The analysis of autonomous quantised heat engines sparked an ongoing debate on the nature of work in autonomous quantum setups [18,19,21,22,[24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41]. Although this debate is not yet settled, the concept of ergotropy [24][25][26] being the quantum analogue of work has gathered strong support in the quantum thermodynamics community.…”

Quantum thermodynamics in a multipartite setting: A resource theory of local Gaussian work extraction for multimode bosonic systems

“…For bosonic systems, for example, restricting to Gaussian states and Gaussian operations has proven to be very fruitful, particularly in the field of quantum information theory with continuous variables [16][17][18]. Similarly, exploring quantum thermodynamics with Gaussian bosonic systems is a promising avenue [19], which we investigate here.…”