Single- versus two-parameter Fisher information in quantum interferometry

TL;DR

This paper compares single- and two-parameter quantum Fisher information in quantum interferometry, clarifies their physical significance, and demonstrates scenarios where single-parameter QFI provides more accurate phase sensitivity bounds.

Contribution

It establishes relations between single- and two-parameter QFI, clarifies their physical roles, and shows practical cases where single-parameter QFI outperforms two-parameter QFI in quantum metrology.

Findings

Single-parameter QFI relates simply to two-parameter Fisher matrix coefficients.

Both single- and two-parameter QFI have physical meaning and attainable bounds.

Single-parameter QFI can outperform two-parameter QFI in certain quantum metrology scenarios.

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 over-optimistic 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.