Proposal for demonstration of long-range cluster state entanglement in the presence of photon loss

Photonic cluster states are a crucial resource for optical quantum computing. Recently a quantum dot single photon source has been demonstrated to produce strings of single photons in a small linear cluster state. Sources of this kind could produce much larger cluster states, but high photon loss rates make it impossible to characterize the entanglement generated by quantum state tomography. We present a benchmarking method for such sources that can be used to demonstrate useful long-range entanglement with currently available collection/detection efficiencies below 1%. The measurement of the polarization state of single photons in different bases can provide an estimate for the three-qubit correlation function ⟨Z X Z ⟩ . This value constrains correlations spanning more than three qubits, which in turn provide a lower bound for the localizable entanglement between any two qubits in the large state produced by the source. Finite localizable entanglement can be established by demonstrating ⟨Z X Z ⟩ >2/3 . This result enables photonic experiments demonstrating computationally useful entanglement with currently available technology.