Lower bound on phase noise of classical states

TL;DR

This paper derives a fundamental lower bound on phase noise for classical states of a single-mode field, highlighting that nonclassical states can surpass this limit and are useful for precise phase measurements.

Contribution

It introduces a new uncertainty relation for number and phase, establishing a lower bound on phase noise for classical states and identifying nonclassical states that violate this bound.

Findings

Derived a lower bound on phase noise for classical states

Identified nonclassical states with less phase noise than classical states

Suggested nonclassical states' potential in precise phase shift measurements

Abstract

An uncertainty relation for the number and phase of a single-mode field state is derived. It is then used to find a lower bound on the phase noise of a classical state. Any state that violates this condition is nonclassical. An example of such a nonclassical state is presented. Because a nonclassical state can have less phase noise than a classical state with the same average photon number, nonclassical states can play a role in the measurement of small phase shifts.