Quantum Metrology concerns the estimation of parameters, like a phase shift in an interferometer, the magnitude of a weak force, or the time duration of a dynamical process, taking into account the quantum character of the systems and processes involved. Quantum mechanics brings in some new features to the process of parameter estimation. The precision of the estimation becomes now intimately related to the possibility of discriminating two different quantum states of the probe corresponding to two different values of the parameter to be estimated. Also, possible measurements must abide by the rules of quantum mechanics. At the same time, quantum properties, like squeezing and entanglement, may help to increase the precision. Recent results demonstrate that hyperentanglement helps to achieve precision beyond the standard limit [1], establish the relationship between quantum metrology and weak measurements [2], and propose a general framework to parameter estimation in open systems [3,4]. This talk will review some recent achievements, involving noisy optical interferometry [3], the quantum speed limit [4], and the detection of weak microwavefields in cavity quantum electrodynamics [5]. For a review, see [6].

[1] S. P. Walborn, A. H. Pimentel, L. Davidovich, and R. L. de Matos Filho, Quantum-Enhanced Sensing from Hyperentanglement, Phys. Rev. A 97, 010301(R) (2018).

[2] G. Bié Alves et al., Achieving metrological precision limits through postselection, Phys. Rev. A 95, 012104 (2017).

[3] B. M. Escher, R. L. de Matos Filho, and L. Davidovich, General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology, Nature Physics 7, 406 (2011).

[4] M. M. Taddei et al., Quantum speed limit for physical processes, Phys. Rev. Lett. 110, 050402

(2013).

[5] M. Penasa et al., Measurement of a microwave field amplitude beyond the standard quantum

limit, Phys. Rev. A 94, 022313 (2016).

[6] L. Davidovich, Lectures at College de France,

http://www.college-de-france.fr/site/jean-dalibard/guestlecturer-2016-02-04-11h00.htm