The protocol is: We start with a supply of identically prepared bipartite non-Gaussian states. The overall protocol then amounts to an iteration of the following basic steps.
- The states will be mixed pairwise locally at 50:50 beam splitters.
- On one of the outputs of each beam splitter, a photon detector distinguishes between the absence and presence of photons. It should be noted that we do not require photon counters that can discriminate between different photon numbers.
- In case of absence of photons at both detectors for a particular pair, one keeps the remaining modes as an input for the next iteration, otherwise the state is discarded. This is one iteration of the protocol which we will continue until we finally end up with a small number of states that closely resemble Gaussian states.
This protocol is presented in the paper: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.67.062320
Specifically, what I am trying to understand is: why does vacuum detection at both outputs lead to distillation? What is the motivation for this step?