A method includes receiving Bell pairs. Photons are obtained in a Greenberger-Horn-Zeilinger (GHZ) state by providing, to a first beam splitter, a photon from a first Bell pair and a photon from a second Bell pair. The first beam splitter is coupled with a first output channel and a second output channel. Obtaining the photons in the GHZ state further includes providing, to a second beam splitter, a photon from a third Bell pair and a photon from a fourth Bell pair. The second beam splitter is coupled with a third output channel and a fourth output channel. Obtaining the photons in the GHZ state further includes providing a photon output from the second output channel as a first input to a detector and a photon output in the third output channel a second input to the first detector.