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 photons in a linear cluster state, but high photon loss rates make it impossible to characterize the entanglement generated by conventional methods. 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%. Measurement of the polarization state of single photons in different bases can provide an estimate for the three-qubit correlation function hZXZi. 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 hZXZi > 2/3 . This result enables photonic experiments demonstrating computationally useful entanglement with currently available technology