nt - p h / 02 02 09 0 v 2 2 9 A ug 2 00 2 Scheme for the generation of an entangled four - photon W - state

We present a scheme to produce an entangled four-photon W-state by using linear optical elements. The symmetrical setup of linear optical elements consists of four beam splitters, four polarization beam splitters and four mirrors. A photon EPR-pair and two single photons are required as the input modes. The projection on the W-state can be made by a four-photon coincidence measurement. Further, we show that by means of a horizontally oriented polarizer in front of one detector the W-state of three photons can be generated. Entanglement is one of the most striking features of quantum mechanics. Entangled state of two or more particles not only provides the possibilities to test quantum mechanics against local hidden theory[1, 2], but also have practical applications in quantum information processing, such as quantum cryptography[3], quantum dense coding [4] and quantum teleportation[5]. Since the GHZ state was introduced to test quantum nonlocality without inequality[8], there has been much interest in the investigation of multiparticle entangled state for more useful applications[8, 9, 10, 11]. In Ref[12], it was shown that there exist two inequivalent classes of three-qubits entangled states, namely the GHZ class and the W class. These two classes are inequivalent because states from one cannot be obtained from the states of the other by local operation and classical communication. Another key difference is that a single-particle trace of the GHZ state result in a maximally mixed state compared with a nonmaximally mixed result for the W state[12]. In Ref[13], the W state has been used to realize the tele-portation of an unknown state probability. Recently a different set of Bell inequality is considered with the purpose of illustrating some difference between the violation of local realism exhibited by the GHZ and W state[14]. More recently, it is shown that the correlation between two qubits selected from a trio prepared in a W state violate the Clauser-Horne-Shimony-Holt inequality more than the correlation between two qubits in any quantum state[15]. In recent experiment, complementary measurement also reveal difference between the GHZ and W state[16] Experiments with entangled photons open a broad field of research. Entangled photon states can be used to test Bell's inequality [17] or to implement quantum information protocols for quantum teleportation [18], quantum dense coding [19] and quantum cryptography [20]. An experimental realization of GHZ-states by means of three or four photons was experimentally observed and used to verify quantum