Quantum metrology is the research field of precision measurements on or employing quantum systems, in which a variety of statistical methods are combined with the rules and tools of quantum theory to determine optimal strategies for directly and indirectly estimating physical quantities. The field of quantum metrology thus encompasses a range of tasks, from the estimation of parameters encoded in unitary transformations such as, for example, times, coupling strengths, phases, frequencies, or squeezing parameters, to the estimation of more complicated quantum channels, state and process tomography, state or channel discrimination problems, and many more.

Research efforts within our group have recently focused on Hamiltonian parameter-estimation problems, employing methods from local’ (or frequentist’) estimation often revolving around the famous quantum Cramér-Rao bound and the quantum Fisher information to obtain lower bounds on the variance of estimated parameters, as well from Bayesian estimation (see, e.g., Chapter 24 of [1] for a pedagogical introduction). We have employed such methods for developing protocols for the metrology-assisted distribution of entanglement in quantum networks [2], and for determining near-optimal and practically easily implementable strategies for estimating parameters characterizing Gaussian transformations in continuous-variable systems using Gaussian states and measurements [3]. In addition, we have been pursuing the development of approaches towards flexible metrology devices simultaneously achieving near-optimal performance at the Heisenberg limit in different estimation tasks [4].

References:

[1] Reinhold Bertlmann and Nicolai Friis, Modern Quantum Theory: From Quantum Mechanics to Entanglement and Quantum Information, Oxford University Press, Oxford, U.K., 2023. ISBN: 9780199683338; DOI: 10.1093/oso/9780199683338.001.0001

[2] Simon Morelli, David Sauerwein, Michalis Skotiniotis, and Nicolai Friis, Metrology-assisted entanglement distribution in noisy quantum networks, Quantum 6, 722 (2022) [arXiv:2110.15627]

[3] Simon Morelli, Ayaka Usui, Elizabeth Agudelo, and Nicolai Friis, Bayesian parameter estimation using Gaussian states and measurements, Quantum Sci. Technol. 6, 025018 (2021) [arXiv:2009.03709]

[4] Nicolai Friis, Davide Orsucci, Michalis Skotiniotis, Pavel Sekatski, Vedran Dunjko, Hans J. Briegel, and Wolfgang Dür, Flexible resources for quantum metrology, New J. Phys. 19, 063044 (2017) [arXiv:1610.09999]