Reexamination of pure qubit work extraction - Frenzel,MF; Jennings,D; Rudolph,T (Physical Review E, 2014)
Many work extraction or information erasure processes in the literature involve the raising and loweringof energy levels via external fields. But even if the actual system is treated quantum mechanically, the fieldis assumed to be classical and of infinite strength, hence not developing any correlations with the system orexperiencing back-actions. We extend these considerations to a fully quantum mechanical treatment by studyinga spin-1/2 particle coupled to a finite-sized directional quantum reference frame, a spin-l system, which modelsan external field. With this concrete model together with a bosonic thermal bath, we analyze the back-actiona finite-size field suffers during a quantum-mechanical work extraction process and the effect this has on theextractable work and highlight a range of assumptions commonly made when considering such processes. Thewell-known semiclassical treatment of work extraction from a pure qubit predicts a maximum extractable workW = kT log 2 for a quasistatic process, which holds as a strict upper bound in the fully quantum mechanical caseand is attained only in the classical limit. We also address the problem of emergent local time dependence in ajoint system with a globally fixed Hamiltonian.