Optimal Quantum-Enhanced Interferometry

TL;DR

This paper investigates the fundamental limits of phase sensitivity in interferometry when the input state is restricted to be a product state, identifying optimal states for fixed photon numbers.

Contribution

It introduces the analysis of phase sensitivity bounds under the restriction of product input states, highlighting the optimal states for fixed photon and mean photon numbers.

Findings

Derived bounds on phase sensitivity with product states

Identified optimal states for fixed photon number

Identified optimal states for fixed mean photon number

Abstract

We analyze the ultimate bounds on the phase sensitivity of an interferometer, given the constraint that the state input to the interferometer's initial 50:50 beamsplitter $B$ is a product state of the two input modes. Requiring a product state is a natural restriction: if one were allowed to input an arbitrary, entangled two-mode state $|\Xi\rangle$ to the beamsplitter, one could generally just as easily input the state $B|\Xi\rangle$ directly into the two modes after the beamsplitter, thus rendering the beamsplitter unnecessary. We find optimal states for a fixed photon number and for a fixed mean photon number.