Unbounded quantum Fisher information in two-path interferometry with finite photon number

TL;DR

This paper demonstrates that certain superposed quantum states can achieve infinite quantum Fisher information with finite photons in two-path interferometry, potentially enhancing quantum measurement precision.

Contribution

It introduces specific superposed states with unbounded quantum Fisher information and shows how to attain maximum information with finite photon resources.

Findings

Superposed NOON states achieve maximum quantum Fisher information.

Certain states exhibit infinite quantum Fisher information with finite photons.

This unbounded information can improve quantum measurement applications.

Abstract

The minimum error of unbiased parameter estimation is quantified by the quantum Fisher information in accordance to the Cram\'{e}r-Rao bound. We indicate that only superposed NOON states by simultaneous measurements can achieve the maximum quantum Fisher information with form $<\hat{N}^{2}>$ for a given photon number distribution by a POVM in linear two-path interferometer phase measurement. We present a series of specified superposed states with infinite quantum Fisher information but with finite average photon numbers. The advantage of this unbounded quantum Fisher information will be beneficial to many applications in quantum technology.