Displaced photon-number entanglement tests

Based on correlations of coherently displaced photon numbers, we derive entanglement criteria for the purpose of verifying non-Gaussian entanglement. Our construction method enables us to verify bipartite and multipartite entanglement of complex states of light. An important advantage of our technique is that the certified entanglement persists even in the presence of arbitrarily high, constant losses. We exploit experimental correlation schemes for the two-mode and multimode scenarios, which allow us to directly measure the desired observables. To detect entanglement of a given state, a genetic algorithm is applied to optimize over the infinite set of our constructed witnesses. In particular, we provide suitable witnesses for several distinct two-mode states. Moreover, a mixed non-Gaussian four-mode state is shown to be entangled in all possible nontrivial partitions.