Classical Inputs and Measurements Enable Phase Sensitivity beyond the Shot-Noise Limit

TL;DR

This paper demonstrates that phase sensitivity beyond the shot-noise limit is achievable with classical inputs and measurements when an external phase reference is used, challenging previous assumptions about fundamental limits.

Contribution

It shows that the shot-noise limit can be surpassed using classical states with external references, supported by quantum Fisher information calculations.

Findings

SNL can be surpassed by a factor of √2 with classical inputs.

External phase references enable phase sensitivity beyond traditional quantum limits.

Applicable in lossy or bright illumination environments.

Abstract

Coherent-state-based phase estimation is a fruitful testbed for the field of precision measurements since coherent states are robust to decoherence when compared with exotic quantum states. The seminal work done by Caves (https://doi.org/10.1103/PhysRevD.23.1693 , Phys. Rev. D 23, 1693 (1981)) stated that the phase sensitivity of a U(2) interferometer fed with a coherent state is limited by the shot-noise limit (SNL). In this Letter, we demonstrate that this bound is not conclusive sensitivity limit and can be broken when the measurement includes an external phase reference. The SNL can be surpassed by a factor of $\sqrt{2}$ and the validity is supported through the calculation of quantum Fisher information. Additionally, we discuss other single-mode Gaussian inputs of which sensitivities are beyond the SNL. Our work shows potential applications for many metological scenarios, particularly when the measured samples immersed in great lossy environments or can withstand bright illumination.