Reexamination of Pure Qubit Work Extraction

TL;DR

This paper investigates quantum work extraction from a spin-1/2 system coupled to a finite quantum reference frame, analyzing back-action effects and the limits of extractable work in a fully quantum setting.

Contribution

It extends classical semi-classical work extraction models to a fully quantum mechanical framework with a finite-sized reference frame.

Findings

Maximum extractable work is W = kT log 2, attained only in the classical limit.

Finite quantum reference frames experience back-action affecting work extraction.

Semi-classical bounds hold as strict upper limits in the quantum case.

Abstract

Many work extraction or information erasure processes in the literature involve the raising and lowering of energy levels via external fields. But even if the actual system is treated quantum mechanically, the field is assumed to be classical and of infinite strength, hence not developing any correlations with the system or experiencing back-actions. We extend these considerations to a fully quantum mechanical treatment, by studying a spin-1/2 particle coupled to a finite-sized directional quantum reference frame, a spin-l system, which models an external field. With this concrete model together with a bosonic thermal bath, we analyse the back-action a finite-size field suffers during a quantum-mechanical work extraction process, the effect this has on the extractable work, and highlight a range of assumptions commonly made when considering such processes. The well-known semi-classical treatment of work extraction from a pure qubit predicts a maximum extractable work W = kT log 2 for a quasi-static process, which holds as a strict upper bound in the fully quantum mechanical case, and is only attained in the classical limit. We also address the problem of emergent local time-dependence in a joint system with globally fixed Hamiltonian.