Linear optical quantum metrology with single photons --- Experimental errors, resource counting, and quantum Cram\'er-Rao bounds

TL;DR

This paper investigates the use of number-path entanglement in linear optical quantum metrology, comparing different interferometric schemes, analyzing resource requirements, calculating quantum bounds, and examining experimental errors to advance super-sensitive measurements.

Contribution

It provides a comprehensive comparison of interferometric schemes using number-path entanglement, including resource analysis, quantum bounds, and error considerations, for improved quantum metrology.

Findings

Number-path entanglement can surpass shot-noise limits in interferometry.

Different schemes have varying resource efficiencies and sensitivities.

Experimental errors significantly impact quantum measurement precision.

Abstract

Quantum number-path entanglement is a resource for super-sensitive quantum metrology and in particular provides for sub-shotnoise or even Heisenberg-limited sensitivity. However, such number-path entanglement has thought to have been resource intensive to create in the first place --- typically requiring either very strong nonlinearities, or nondeterministic preparation schemes with feed-forward, which are difficult to implement. Recently in [Phys. Rev. Lett. 114, 170802 (2015)] we showed that number-path entanglement from a BosonSampling inspired interferometer can be used to beat the shot-noise limit. In this manuscript we compare and contrast different interferometric schemes, discuss resource counting, calculate exact quantum Cram\'er-Rao bounds, and study details of experimental errors.