Exploration Of Multiphoton Entangled States And Bell-type Inequalities For Multiqubit Systems

As a tangible physical resource, quantum entanglement is of the chief differences between quantum and classical mechanics. The study of quantum entanglement is without a doubt a significant problem to the development of quantum information processing. This thesis mainly study the exploration of multiphoton entangled states and Bell-type inequalities for multiqubit systems. The results are as follows:1. We present an efficient scheme for the preparing and purifying of the four-photon Greenberger-Horne-Zeilinger(GHZ) state based on parametric down-conversion sources, Kerr media and linear optics. We first describe how to create a four-photon GHZ state in both polarization and spatial degrees of freedom from two pairs. Then, in the presence of depolarization noise our scheme is capable of purifying the polarization entanglement using spatial entanglement.2. We present an efficient scheme of generation of six-photon hyperentangled states with polarization entanglement and spatial entanglement. We here consider three pairs of entangled photons emitted by the parametric down-conversion source and design quantum circuit to evolve these photons. Because it contains all possible cases, the present scheme is efficient.3. We propose a fruitful scheme for exploring multiphoton entangled states based on linear optics and weak nonlinearities. The present method is feasible because there are only small phase shifts 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.4. A method for exploring photon-number entangled states with weak nonlinearities is described. In the present architecture, we suggest that the maximal phase shift induced in the process of interaction between photons is proportional to photon numbers. Also, in the absence of decoherence we analyze maximum error probability and show its feasibility with current technology.5. 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.6. Based on Clauser-Horne-Shimony-Holt inequality, we show a fruitful method to exploit Bell-type inequalities for multiqubit systems. These 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 then discuss quantum violations for generalized GHZ(GGHZ) states and two kinds of mixed entangled states. Also, as an example, we reveal relationship between quantum nonlocality and four-partite entanglement for four-qubit GGHZ states.