• DOI:10.1103/PRXQuantum.2.020322
• Corpus ID: 227118770

Optimal Quantum Thermometry with Coarse-Grained Measurements

@article{Hovhannisyan2020OptimalQT,
  title={Optimal Quantum Thermometry with Coarse-Grained Measurements},
  author={Karen V. Hovhannisyan and M. R. V. J{\o}rgensen and Gabriel T. Landi and {\'A}lvaro M. Alhambra and Jonatan Bohr Brask and Mart{\'i} Perarnau-Llobet},
  journal={arXiv: Quantum Physics},
  year={2020}
}

• K. Hovhannisyan, M. R. Jørgensen, +3 authors M. Perarnau-Llobet
• Published 20 November 2020
• Physics
• arXiv: Quantum Physics

Precise thermometry for quantum systems is important to the development of new technology, and understanding the ultimate limits to precision presents a fundamental challenge. It is well known that optimal thermometry requires projective measurements of the total energy of the sample. However, this is infeasible in even moderately-sized systems, where realistic energy measurements will necessarily involve some coarse graining. Here, we explore the precision limits for temperature estimation when only coarse-grained measurements are available. Utilizing tools from signal processing, we derive the structure of optimal coarse-grained measurements and find that good temperature estimates can generally be attained even with a small number of outcomes. We apply our results to many-body systems and non-equilibrium thermometry. For the former, we focus on interacting spin lattices, both at and away from criticality, and find that the Fisher-information scaling with system size is unchanged after coarse-graining. For the latter, we consider a probe of given dimension interacting with the sample, followed by a measurement of the probe. We derive an upper bound on arbitrary, non-equilibrium strategies for such probe-based thermometry and illustrate it for thermometry on a Bose-Einstein condensate using an atomic quantum-dot probe.