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Experimental generation of a high-fidelity four-photon linear cluster state

Cluster state plays a crucial role in the one-way quantum computation. Here, we propose and experimentally demonstrate a new scheme to prepare an ultrahigh-fidelity four-photon linear cluster state via spontaneous parametric down-conversion process. The state fidelity is measured to be $0.9517\pm0.0027$. Our scheme can be directly extended to more photons to generate N-qubit linear cluster state. Furthermore, our scheme is optimal for generating photonic linear cluster states in the sense of achieving the maximal success probability and having the simplest strategy. The key idea is that the photon pairs are prepared in some special non-maximally entangled states instead of the normal Bell states. To generate a 2N-qubit linear cluster state from N pairs of entangled photons, only (N-1) Hong-Ou-Mandel interferences are needed and a success probability of $(\frac{1}{4})^{N-1}$ is achieved.