Generation of energy-entangled W states

Tripartite entangled states, such as Greenberger-Horne-Zeilinger (GHZ) and W states, are appealing for tests of fundamental aspects of quantum mechanics, as well as for implementations of quantum communication protocols. While the information is typically encoded in the polarization or path of the photons, we propose a feasible scheme to generate W states that are entangled in the energy degree of freedom. This is achieved by propagating photon pairs generated by parametric fluorescence in a linear optical circuit and post-selecting on the output channels. Such source can be easily integrated, profiting from high stability and a compact footprint. We also present a simple protocol to characterize the generated tripartite state, which is based on the reduced density matrix approach. Unexpectedly, although we rely on the energy degree of freedom, the full state tomography does not require any frequency conversion.