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QI: Fachverband Quanteninformation
QI 32: Quantum Sensing and Metrology
QI 32.6: Talk
Friday, March 22, 2024, 11:15–11:30, HFT-FT 131
Quantum metrology in the finite-sample regime — Johannes Jakob Meyer1, •Sumeet Khatri1, Daniel Stilck França1,2,3, Jens Eisert1,4,5, and Philippe Faist1 — 1Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, Berlin, Germany — 2Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark — 3Ecole Normale Superieure de Lyon, Lyon, France — 4Helmholtz-Zentrum für Materialien und Energie, Berlin, Germany — 5Fraunhofer Heinrich Hertz Institut, Berlin, Germany
In quantum metrology, the ultimate precision of estimating an unknown parameter is often stated in terms of the Cramér-Rao bound. Yet, the latter is no longer guaranteed to carry operational meaning in the regime of few measurement samples. We instead propose to quantify the quality of a metrology protocol by the probability of obtaining an estimate with a given accuracy. This approach, which we refer to as probably approximately correct (PAC) metrology, ensures operational significance in the finite-sample regime. The accuracy guarantees hold for any value of the unknown parameter, unlike the Cramér-Rao bound which assumes it is approximately known. We establish a strong connection to multi-hypothesis testing with quantum states, which allows us to derive an analogue of the Cramér-Rao bound which contains explicit corrections relevant to the finite-sample regime and apply our framework to phase estimation with an ensemble of spin-1/2 particles. Our operational approach allows the study of quantum metrology in the finite-sample regime and opens up new avenues for research at the interface of quantum information theory and quantum metrology.
Keywords: finite-sample quantum metrology; non-asymptotic quantum metrology; hypothesis testing; single-shot quantum information; phase estimation