Single- versus two-parameter Fisher information in quantum interferometry
Stefan Ataman
Abstract
In this paper we reconsider the single-parameter quantum Fisher information (QFI) and compare it with the two-parameter one. We find simple relations connecting the single-parameter QFI (both in the asymmetric and symmetric phase shift cases) to the two-parameter Fisher matrix coefficients. Following some clarifications about the role of an external phase [Phys. Rev. A 85, 011801(R) (2012)], the single-parameter QFI and its overoptimistic predictions have been disregarded in the literature. We show in this paper that both the single- and two-parameter QFI have physical meaning, and their predicted quantum Cram\'er-Rao bounds are often attainable with the appropriate experimental setup. Moreover, we give practical situations of interest in quantum metrology, where the phase sensitivities of a number of input states approach the quantum Cram\'er-Rao bound induced by the single-parameter QFI, outperforming the two-parameter QFI.