Unbiased estimation of an optical loss at the ultimate quantum limit with twin-beams

Loss measurements are at the base of spectroscopy and imaging, thus permeating all the branches of science, from chemistry and biology to physics and material science. However, quantum mechanics laws set the ultimate limit to the sensitivity, constrained by the probe mean energy. This can be the main source of uncertainty, for example when dealing with delicate systems such as biological samples or photosensitive chemicals. It turns out that ordinary (classical) probe beams, namely with Poissonian photon number distribution, are fundamentally inadequate to measure small losses with the highest sensitivity. It is known that quantum-correlated pair of beams, named twin-beam state, allows surpassing this classical limit. Here we demonstrate they can reach the ultimate sensitivity for all energy regimes (even less than one photon per mode) with the simplest measurement strategy. One beam of the pair addresses the sample, while the second one is used as a reference to compensate both for classical drifts and for fluctuation at the most fundamental quantum level. This capability of selfcompensating for unavoidable instability of the sources and detectors allows also to strongly reduce the bias in practical measurement. Moreover, we report the best sensitivity per photon ever achieved in loss estimation experiments.