Figure 2

Results of the multiparameter quantum estimation in a superresolution imaging scenario with a photon-pair source. (a) Experimental setup for generating a pair of photons in two adjacent modes (PBS, polarizing beam splitter; λ / 2 , half-wave plate; BD, calcite beam displacer). Using an | h v ⟩ photon pair and reconfiguring the positions of the retroreflectors in the interferometer, we generate the two-photon state expected in the imaging experiment for a set of values of source separation ϵ . The output single mode fiber (SMF) face is imaged onto the I-sCMOS sensor (see Supplemental Material [41] or Ref. [43] for details of I-sCMOS sensor operation and construction) photocathode so that the beam has a flat wave front with 1 / e 2 diameter of 100 μ m . The camera registers cross-coincidences (as coincidences between regions A–C, A–D, B–C, and B–D) and double events (as coincidences between regions A–B or C–D). (b) Spatially resolved cross-coincidences (top) and double events (bottom) along with fitted model with Gaussian mode shape for subsequent values of ϵ corresponding to data points in (c) and (d). Color scale for each map is normalized separately to highlight shape intricacies. (c) Precision of estimation of ϵ for the ρ ⊗ 2 state and (d) precision of estimation of the centroid position x 0 as a function of source separation ϵ . The collective 2P scheme provides an enhancement in estimation of ϵ while preserving the precision of centroid estimation. The ultimate precision limit given by the quantum Cramér-Rao bound is denoted by qCRB, and for the precision of centroid estimation in (d) it overlaps with the precision obtained with the protocols we employ. Theoretical curves are obtained from numerically evaluated FI. Error bars correspond to 1 standard deviation of results obtained from each data set containing 1000 coincidences (see Supplemental Material for details [41]).