Phase-noise protection in quantum-enhanced differential interferometry

Differential interferometry (DI) with two coupled sensors is a most powerful approach for precision measurements in presence of strong phase noise. However DI has been studied and implemented only with classical resources. Here we generalize the theory of differential interferometry to the case of entangled probe states. We demonstrate that, for perfectly correlated interferometers and in the presence of arbitrary large phase noise, sub-shot noise sensitivities -- up to the Heisenberg limit -- are still possible with a special class of entangled states in the ideal lossless scenario. These states belong to a decoherence free subspace where entanglement is passively protected. Our work pave the way to the full exploitation of entanglement in precision measurements in presence of strong phase noise.