Preparation of $km$-photon concatenated GHZ states for observing distinct quantum effects at macroscopic scale

As a class of multipartite entangled states, the multipartite concatenated GHZ (C-GHZ) states remain superior stability under the influence of decoherence. We propose two scalable experimental realization of the multiphoton C-GHZ states based on the entanglers of multiphoton GHZ state. Given a $km$-photon GHZ state as an input state, if $m$ is odd, one can create a $km$-photon C-GHZ state. Also, generally, we design a scheme to prepare $km$-photon C-GHZ states from $km$ single-photon states by using $k$ entanglers of $m$-photon GHZ state and $k$ $m$-control Toffoli gates.

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