Generating Greenberger-Horne-Zeilinger states using multiport splitters

Abstract

Symmetric multiport splitters are versatile tools in optical quantum information processing. They can be used for studying multiparticle scattering, for studying distinguishability and mixedness, and also for the generation of multipartite entangled quantum states. Here, we show that $N$-photon $N$-mode Greenberger-Horne-Zeilinger (GHZ) states can be generated using symmetric multiport beam splitters. Varying the input states' internal degrees of freedom and postselecting onto certain photon-number distributions allows the probabilistic generation of GHZ states with arbitrary photon numbers. We present two schemes, one for odd and one for even numbers of photons, to generate GHZ states using symmetric multiport splitters and compare them to a strategy utilizing a $2N$-port network as well as the standard postselection method.