Entanglement-enhanced measurement of a completely unknown optical phase

Abstract

Precise interferometric measurement is vital to many scientific and technological applications. Using quantum entanglement allows interferometric sensitivity that surpasses the shot-noise limit (SNL)1, 2. To date, experiments demonstrating entanglement-enhanced sub-SNL interferometry3, 4, 5, 6, and most theoretical treatments7, 8, 9, 10, 11, 12, 13, have addressed the goal of increasing signal-to-noise ratios. This is suitable for phase-sensing—detecting small variations about an already known phase. However, it is not sufficient for ab initio phase-estimation—making a self-contained determination of a phase that is initially completely unknown within the interval [0, 2π). Both tasks are important2, but not equivalent. To move from the sensing regime to the ab initio estimation regime requires a non-trivial phase-estimation algorithm14, 15, 16, 17. Here, we implement a ‘bottom-up’ approach, optimally utilizing the available entangled photon states, obtained by post-selection5, 6. This enables us to demonstrate sub-SNL ab initio estimation of an unknown phase by entanglement-enhanced optical interferometry.