Central Moments of Squeezed States: A Coincidence Statistics Analogue

As a subset of quantum optics, single photons are one of the competing physical resources for quantum information processing. When used as carriers of quantum information, they have no equal. For the processing of quantum information, single photons have proven difficult to scale beyond the order of ⇠ 10 photons. The lack of single-photon-level interaction has led to creative approaches which rely on postselection to filter the possible measured outcomes to those which appear as though
interaction occurred. This approach of post-selection leans heavily on the ability to
not only generate but also detect scores of single photons simultaneously and with
near perfect efficiency. Our work relaxes the emphasis which has been placed on single
photons for quantum information processing to that of states with, in principle, an
arbitrary number of photons. Central moment expectations on two-mode squeezed
states are shown to exhibit post-selection behavior which reflects the single-photon
counterpart. These measures are proven to be robust to loss and return entangled
state statistics on average. With naive estimation of the central moment, states
with ~ 20 modes are within reach with current technology, closing the gap between quantum states which can and cannot be classically simulated.