title: Ultimate Precision Limits for Noisy Frequency Estimation.
abstract: Quantum metrology protocols allow us to surpass precision limits typical to classical statistics. However, in recent years, no-go theorems have been formulated, which state that typical forms of uncorrelated noise can constrain the quantum enhancement to a constant factor and, thus, bound the error to the standard asymptotic scaling. In particular, that is the case of time-homogeneous (Lindbladian) dephasing and, more generally, all semigroup dynamics that include phase covariant terms, which commute with the system Hamiltonian. We show that the standard scaling can be surpassed when the dynamics is no longer ruled by a semigroup and becomes time inhomogeneous. In this case, the ultimate precision is determined by the system short-time behavior, which when exhibiting the natural Zeno regime leads to a nonstandard asymptotic resolution. In particular, we demonstrate that the relevant noise feature dictating the precision is the violation of the semigroup property at short time scales, while non-Markovianity does not play any specific role.
authors.affiliation: Institute of Theoretical Physics, Universität Ulm, Albert-Einstein-Allee 11D-89069 Ulm, Germany.
authors.forename: Andrea
authors.initials: A
authors.lastname: Smirne
authors.affiliation: ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain.
authors.forename: Jan
authors.initials: J
authors.lastname: Kołodyński
authors.affiliation: Institute of Theoretical Physics, Universität Ulm, Albert-Einstein-Allee 11D-89069 Ulm, Germany.
authors.forename: Susana F
authors.initials: SF
authors.lastname: Huelga
authors.affiliation: Faculty of Physics, University of Warsaw, 02-093 Warszawa, Poland.
authors.forename: Rafał
authors.initials: R
authors.lastname: Demkowicz-Dobrzański