Reexamination of Pure Qubit Work Extraction

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.

16 pages, 11 figures; v2: updated figures and extended discussion; v3: changed title and minor updates, published in PRE

References in corpus (7)

• Reference frames, superselection rules, and quantum information
• The thermodynamic meaning of negative entropy
• Dynamics of a Quantum Reference Frame
• Extracting work from quantum systems
• Quantum Reference Frames and the Classification of Rotationally-Invariant Maps
• Dynamics of a quantum reference frame undergoing selective measurements and coherent interactions
• The smallest possible heat engines

Cited by in corpus (8)

• Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
• Coherence-enhanced efficiency of feedback-driven quantum engines
• Clock-Driven Quantum Thermal Engines
• High-capacity and high-power collective charging with spin chargers
• Heat and charge transport measurements to access single-electron quantum characteristics
• Double quantum-dot engine fueled by entanglement between electron spins
• Dynamics of a strongly coupled quantum heat engine -- computing bath observables from the hierarchy of pure states
• Fully quantum second-law--like statements from the theory of statistical comparisons