One-step deterministic polarization-entanglement purification using spatial entanglement

We present a one-step deterministic entanglement purification protocol with linear optics and postselection. Compared with the Simon-Pan protocol [C. Simon and J. W. Pan, Phys. Rev. Lett. 89, 257901 (2002)], this one-step protocol has some advantages. First, it can obtain a maximally entangled pair from each photon pair with only one step, instead of improving the fidelity of less-entangled photon pairs by performing the entanglement purification process repeatedly in other protocols. Second, it works in a deterministic way, not a probabilistic one, which greatly reduces the number of entanglement resources needed. Third, it does not require the polarization state be entangled; only spatial entanglement is needed. Moreover, it is feasible with current techniques [J. W. Pan, S. Gasparonl, R. Ursin, G. Weihs, and A. Zellinger, Nature (London) 423, 417 (2003)]. All these advantages make this one-step protocol more convenient than others in quantum-communication applications.