Regensburg 2022 – scientific programme
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QI: Fachverband Quanteninformation
QI 8: Quantum Sensors and Metrology
QI 8.7: Talk
Wednesday, September 7, 2022, 17:00–17:15, H9
Quantum metrology in the non-asymptotic regime — Johannes Jakob Meyer1, Sumeet Khatri1, •Philippe Faist1, Daniel Stilck-França2, Giacomo Guarnieri1, and Jens Eisert1,3,4 — 1Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany — 2Univ Lyon, ENS Lyon, UCBL, CNRS, Inria, LIP, F-69342, Lyon Cedex 07, France — 3Fraunhofer Heinrich Hertz Institute, 10587 Berlin, Germany — 4Helmholtz-Zentrum Berlin für Materialien und Energie, 14109 Berlin, Germany
The main concern of quantum metrology is to determine how we can achieve the best possible precision in estimating parameters of physical processes. One of the main tools used in the field is the Quantum Cramér-Rao bound. However, it is a relation that is only tight and meaningful asymptotically and, conversely, too optimistic for finite numbers of experimental repetitions. We analyze how a change of perspective to an operationally motivated measure of estimation success can be used to achieve more meaningful bounds. We show that the measure can be evaluated using a semidefinite program and detail how it can be used to establish minimax guarantees against any prior distribution of the underlying parameter. We focus on the analysis of group-covariant estimation on pure states, which is relevant because of its relation to phase estimation. We prove that the optimal measurement in this setting is given by the pretty good measurement and exhibit a construction of a probe state that numerically saturates the optimal asymptotic minimax rate.