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

摘要

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