Gaussian Thermal Operations and The Limits of Algorithmic Cooling

Abstract

The resource theory of thermal operations allows one to investigate the ultimate possibilities of quantum states and of nanoscale thermal machines. Whilst fairly general, these results 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 operations acting on an arbitrary number of bosonic modes, which turn out to be all embeddable in a Markovian dynamics, and derive a simple geometric criterion establishing 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.

Resource Preservability

“…This important feature of resource theory provides an identification allowing not just detection but also comparison. Various resource theories have been reported for, but not limited to, entanglement [3,13], coherence [14,15], nonlocality [7,16], steering [10,[17][18][19], asymmetry [20,21], and athermality [22][23][24][25][26][27]. There are also general features of resource theories [28][29][30][31][32][33][34][35][36][37][38][39][40].…”

Thermodynamic optimization of quantum algorithms: on-the-go erasure of qubit registers

“…Algorithmic cooling is the process of producing cold (that is, approximately pure) qubits [28]. There are approaches that extract entropy from a target system by coupling it to thermal baths in an approach called heat-bath algorithmic cooling [29][30][31]. Our optimizations in erasure distinguish themselves from algorithmic cooling in in that they are not primarily about the production of pure qubits but rather about reducing the thermodynamic cost of said erasure using entanglement as a further resource.…”

Thermodynamic resources in continuous-variable quantum systems

“…From a practical standpoint, the interactions that are most feasible on bosonic systems are those that are quadratic in the quadrature operators-so-called Gaussian operations. Recent work, where arbitrary quadratic local and interaction Hamiltonians are considered, shows that energyconserving interactions under this constraint effectively decompose into independent processes involving bosonic passive linear interactions between modes of identical frequencies 26 . Such interactions correspond to circuits of beam-splitters and phaseshifters in optics.…”