$pi$-corrected Heisenberg limit

The Heisenberg limit is the fundamental bound for the precision of estimation in terms of the amount of resources N used in an experiment (where resources may be understood, depending on the context, as number of photons, number of quantum gates, total energy, total time of interrogation etc.). It provides better scaling with N comparing to situations where resources are used separately. In this talk I will show that conventional Heisenberg limit (derived from the properties of the quantum Fisher information), is not operationally meaningful and should be rescaled by constant factor π.