We propose two schemes to generate four-photon polarization-entangled states from the secondorder emission of the spontaneous parametric down-conversion process. By using linear optical elements and the coincidence-detection, the four indistinguishable photons emitted from parametric down-conversion source result in the Greenberger-Horne-Zeilinger (GHZ) state or the superposition of two orthogonal GHZ states. For this superposition state, under particular phase settings we analyze the quantum correlation function and the local hidden variable (LHV) correlation. As a result, the Bell inequality derived from the LHV correlation is violated with the visibility larger than 0.442. It means that the present four-photon entangled state is therefore suitable for testing the LHV theory. PACS numbers: 03.67.-a, 03.67.Bg, 03.67.Lx, 42.50.Ex I. INTRODUCTIONAs a quantum resource, multiphoton entanglement [1, 2] plays an important role in both theoretical studies and experimental techniques. One of the attractive aspects of this field is how to generate the desired multiphoton entangled states [3][4][5][6][7][8][9][10][11][12][13]. Since a spontaneous parametric down-conversion (PDC) [14][15][16][17] source is capable of creating pairs of entangled photons, in general, a standard method of generating the multiphoton entanglement is to evolve the pairs emitted from respective source with a set of passive optical elements [2]. For this purpose, it is crucial to suppress undesired multipair emissions and enhance the collection efficiency of the entangled photon pairs.A higher-order emission of the PDC source [18-24] is related to a twin-beam multiphoton entangled state. For the second-order emission, it has been shown that [22], when the duration of the pump pulse is much shorter than the coherence time of the photons, the emitted state can be described as an indistinguishable twin-beam four-photon entangled state (a genuine four-partite entanglement) rather than two independent pairs. Based on such four-photon emission, Weinfurter andŻukowski [25] proposed a novel method of generating four-photon polarization entangled state. By using several linear optical elements, a kind of four-photon polarization entangled state can be obtained directly in PDC process, instead of recombining two entangled-photon pairs. This four-photon entangled state can be used to test the local hidden variable (LHV) theory [25]. Later, it leads to the following discussion on four-photon entanglement in two-crystal geometry by Li and Kobayashi [26].In this paper, we at first focus on the generation of two particular types of four-photon entangled states from the second-order emission of the PDC source. The output states are quite different from the previous ones because of the interference at an additional polarizing beam splitter (PBS) before the fourfold coincidence detection. We then compare LHV correlation function and quantum correlation function under particular phase settings. The result is that the quantum violation of the present four-photon enta...

We propose a fruitful scheme for exploring multiphoton entangled states based on linear optics and weak nonlinearities. Compared with the previous schemes the present method is more feasible because there are only small phase shifts instead of a series of related functions of photon numbers in the process of interaction with Kerr nonlinearities. In the absence of decoherence we analyze the error probabilities induced by homodyne measurement and show that the maximal error probability can be made small enough even when the number of photons is large. This implies that the present scheme is quite tractable and it is possible to produce entangled states involving a large number of photons.

Quantum nonlocality of generic family of four-qubit entangled pure states * Ding Dong(丁 东) a)b) , He Ying-Qiu(何英秋) a) , Yan Feng-Li(闫凤利) a) † , and Gao Ting(高 亭) c) ‡

Based on Clauser-Horner-Shimony-Holt inequality, we show a fruitful method to exploit Bell inequalities for multipartite qubit systems. These Bell inequalities are designed with a simpler architecture tailored to experimental demonstration. Under the optimal setting we derive a set of compact Mermin-type inequalities and discuss quantum violations for generalized Greenberger-Horne-Zeilinger (GGHZ) states. Also, we reveal relationship between quantum nonlocality and four-partite entanglement for four-qubit GGHZ states.

By calculating entanglement measures and quantum violation of Bell-type inequality, we reveal the relationship between entanglement measure and the amount of quantum violation for a family of four-qubit entangled states. It has been demonstrated that the Bell-type inequality is completely violated by these four-qubit entangled states. The plot of entanglement measure as a function of the expectation value of Bell operator shows that entanglement measure first decreases and then increases smoothly with increasing quantum violation.