Środowiskowe Seminarium z Informacji i Technologii Kwantowych

We address the question whether the super-Heisenberg scaling for quantum estimation is indeed realizable. We unify the results of two approaches. In the first one, the original system is compared with its copy rotated by the parameter dependent dynamics. If the parameter is coupled to the one-body part of the Hamiltonian the precision of its estimation is known to scale at most as N−1 (Heisenberg scaling) in terms of the number of elementary subsystems used, N. The second approach compares the overlap between the ground states of the parameter dependent Hamiltonian.In critical systems this often leading to an apparent super-Heisenberg scaling. However, we point out that if one takes into account the scaling of time needed to perform the necessary operations, i.e. ensuring adiabaticity of the evolution, the Heisenberg limit given by the rotation scenario is recovered. We illustrate the general theory on a ferromagnetic Heisenberg spin chain example. We discuss universal scaling predictions of the estimation precision offered by natural local observables, both at zero and finite temperatures, and support them with numerical simulations in the model. We explicitly derive that the Heisenberg limit is recovered when time needed for preparation of quantum states involved is taken into account.M.M. Rams, P. Sierant, O. Dutta, P. Horodecki, J. Zakrzewski, Phys. Rev. X 8, 021022 (2018)