Figure 4

Absolute quantum advantage in absorption measurement. (a) Γ is the ratio of the variance of an absorption estimate for the ideal classical scheme, to our experimental measurement. (b) Normalised optical exposure for equal precision, computed from the ratio between the number of photons probing the sample in a particular scheme and in the best direct classical scheme attaining the same estimation precision by increasing the illumination. In both plots: the red solid lines correspond to the ideal classical limit, the red dotted lines correspond to a classical state detected with the same 90% efficiency as in our setup, and the red dashed lines correspond to the example of a differential classical measurement where a laser is split on a 50:50 beamsplitter (Fig. 1(b)) and therefore quantum fluctuations are un-correlated. The yellow line corresponds to the theoretical limit achievable by our system, taking into account the measured rate of classical fluctuations and the arms efficiencies (See Supplementary material). The blue dots with error bars correspond to the experimental data using the quantum corrected measurement. The green asterisks correspond a classical measurement with our setup, using only the single photons generated from downconversion passing through the sample in Arm 1 and ignoring any correlated data in Arm 2. And finally the blue shadowed area highlight the absolute quantum advantage that is detected. Error bars correspond to the standard error on the related quantities taking into account both the uncertainty on the precision of the measurement and the uncertainty on the efficiency of the camera following error propagation on equations (3) and (4). The blue lines correspond to best-fit to the theory, with extra parameters corresponding to eventual super-poissonian non-deterministic and deterministic noise in each fluorescence beam, and to camera noise. All data and curves in both plots normalise to PPE to the sample. N.b. the first point of each plot is obtained with only the HWP as a sample i.e. removing the PBS.