Thermodynamic work cost of quantum estimation protocols

Abstract

We discuss thermodynamic work cost of various stages of a quantum estimation protocol: probe and memory register preparation, measurement and extraction of work from post-measurement states. We consider both (i) a multi-shot scenario, where average work is calculated in terms of the standard Shannon entropy and (ii) a single-shot scenario, where deterministic work is expressed in terms of min- and max-entropies. We discuss an exemplary phase estimation protocol where estimation precision is optimized under a fixed work credit (multi-shot) or a total work cost (single-shot). In the multi-shot regime precision is determined using the concept of Fisher information, while in the single-shot case we advocate the use of confidence intervals as only they can provide a meaningful and reliable information in a single-shot experiment, combining naturally with the the concept of deterministic work.

25 pages, 3 figures, published version

References in corpus (15)

• Quantum metrology from a quantum information science perspective
• Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
• Quantum information can be negative
• Optimal Quantum Phase Estimation
• The thermodynamic meaning of negative entropy
• True precision limits in quantum metrology
• Multiparameter Gaussian Quantum Metrology
• Phase estimation without a priori knowledge in the presence of loss
• Gibbs-Preserving Maps outperform Thermal Operations in the quantum regime
• Fundamental work cost of quantum processes
• Robust error bars for quantum tomography
• Quantum Reference Frames and Their Applications to Thermodynamics
• Energy-efficient quantum frequency estimation
• Parameter estimation in the presence of the most general Gaussian dissipative reservoir
• Quantum Coarse-Graining: An Information-Theoretic Approach to Thermodynamics

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