Maximal quantum Fisher information for phase estimation without initial parity

TL;DR

This paper analyzes the ultimate phase estimation precision in Mach-Zehnder interferometers using various input states, providing analytical formulas and strategies to mitigate photon loss effects for improved quantum measurement accuracy.

Contribution

It derives a general analytical expression for quantum Fisher information and identifies optimal initial parity and phase-matching conditions under photon loss.

Findings

Analytical expression for quantum Fisher information in Mach-Zehnder interferometers.

Strategies to restore phase accuracy under symmetric and asymmetric photon losses.

Identification of optimal initial parity for enhanced phase estimation.

Abstract

Mach-Zehnder interferometer is a common device in quantum phase estimation and the photon losses in it are an important issue for achieving a high phase accuracy. Here we thoroughly discuss the precision limit of the phase in the Mach-Zehnder interferometer with a coherent state and a superposition of coherent states as input states. By providing a general analytical expression of quantum Fisher information, the phase-matching condition and optimal initial parity are given. Especially, in the photon loss scenario, the sensitivity behaviors are analyzed and specific strategies are provided to restore the phase accuracies for symmetric and asymmetric losses.