Conclusive Precision Bounds for SU(1,1) Interferometers

TL;DR

This paper analyzes the quantum Fisher information bounds in SU(1,1) interferometers, revealing how phase configurations and input states affect phase sensitivity and establishing the importance of the QFIM in precise quantum phase estimation.

Contribution

It demonstrates the equivalence of phase averaging and two-parameter estimation in SU(1,1) interferometers and provides phase sensitivity calculations for various input states.

Findings

Phase averaging yields identical QFI for vacuum inputs across configurations.

QFIM is essential for accurate phase sensitivity in general cases.

Phase sensitivity varies with input states and phase configurations.

Abstract

In this paper, we revisit the quantum Fisher information (QFI) calculation in SU(1,1) interferometer considering different phase configurations. When one of the input modes is a vacuum state, we show by using phase averaging, different phase configurations give same QFI. In addition, by casting the phase estimation as a two-parameter estimation problem, we show that the calculation of the quantum Fisher information matrix (QFIM) is necessary in general. Particularly, within this setup, the phase averaging method is equivalent to a two parameter estimation problem. We also calculate the phase sensitivity for different input states using QFIM approach.