## Jan Haase, Universität Ulm

Whenever one is tempted to employ a quantum system for any kind of applications, the focus usually lies on two properties setting it apart from a system described by a classical theory, namely the coherent superposition of different quantum states and entanglement between two ore more constituents forming the system. For the aim of parameter estimation, it is known that a neat employment of these resources pushes the achievable precision beyond the classical limit by squaring the gain one obtains in a classical configuration with repeated data acquisition. Indeed, the error of such an estimate is inversely proportional to the number N of acquired data sets instead of its square root. In principle, measurements utilizing quantum features can thus be drastically more precise [1]. However, depending on the characteristics of the noise this advantage is decreased or even removed [2–4]. Nevertheless, in the asymptotic limit of many probes, it was shown that the quantum advantage can be partially restored under the assumption of phase-covariant dynamics, i.e. the action of the noise commutes with the unitary parameter encoding, and furthermore the short time evolution of the probes departs from a time homogeneous (semigroup) dynamic [5]. However, when going beyond these assumptions, the whole picture is still unknown.

I will show that all the previously derived limits of precision derived for phenomenology stated master equations, can be reproduced by the microscopically motivated spin-boson model. In particular, the magnitude of the gain can be ascribed to both the geometry of the noise and interplay of different timescales involved in the evolution. In any case, the scaling of the quadratic error ∆2ω in the frequency estimate ω is described by an exponent η which is between 1 for the classical case and 2 for the optimal quantum case, such that the error is ∆2ω ∼ N−η. Besides reporting the discovery of the best exponent η = 7/4 known so far, I will comment on the effect of terms breaking the phase-covariance in frequency estimation schemes, in particular their short time limit and the influence of the parameter dependent decay rates [6].

[1] V. Giovannetti, S. Lloyd, and L. Maccone, Science 306, 1330 (2004).

[2] S. F. Huelga, C. Macchiavello, T. Pellizzari, A. K. Ekert, M. B. Plenio, and J. I. Cirac, Phys. Rev. Lett. 79, 3865 (1997).

[3] B. M. Escher, R. L. de Matos Filho, and L. Davidovich, Nat. Phys. 7, 406 (2011).

[4] R. Demkowicz-Dobrza´nski, J. Kołody´nski, and M. Guta, Nat. Commun. 3, 1063 (2012).

[5] A. Smirne, J. Kołody´nski, S. F. Huelga, and R. Demkowicz-Dobrza´nski, Phys. Rev. Lett. 116, 120801 (2016).

[6] J. F. Haase, A. Smirne, J. Kołody´nski, R. Demkowicz-Dobrza´nski and S. F. Huelga, arXiv:1710.04673