  The dynamics of open quantum systems is generally described by a master
equation, which describes the loss of information into the environment. By
using a simple model of uncoupled emitters, we illustrate how the recovery of
this information depends on the monitoring scheme applied to register the decay
clicks. The dissipative dynamics, in this case, is described by pure-state
stochastic trajectories and we examine different unravelings of the same master
equation. More precisely, we demonstrate how registering the sequence of clicks
from spontaneously emitted photons through a linear optical interferometer
induces entanglement in the trajectory states. Since this model consists of an
array of single-photon emitters, we show a direct equivalence with Fock-state
boson sampling and link the hardness of sampling the outcomes of the quantum
jumps with the scaling of trajectory entanglement.
