Optimal Transmission Estimation Using Macroscopic Quantum States of Light*

It is well known that the use of quantum resources can reduce the uncertainty in parameter estimation. Here we focus on the estimation of transmission, which is needed for a number of applications such as the calibration of a detector's quantum efficiency, ellipsometry, plasmonic sensing, measurement of absorption spectra, etc. Enhancing transmission estimation is typically done by either increasing the number of photons used to probe the system via high power classical states or using low power quantum states that give the most information per photon. We show that the bright two-mode squeezed state, a macroscopic quantum state that can be generated with a large number of photons, approaches the known minimum uncertainty in transmission estimation for any state in the limit of large levels of squeezing. Our experimental  results show that we can saturate the quantum Cramér-Rao bound for transmission estimation with a bright two-mode squeezed state using an optimized intensity difference measurement and that this simple measurement is robust to extraneous losses in the experiment. Thus, we show that it is possible to use a quantum states to both probe with a large number of photons and to have more information gained per photon than a classical state.