Superposition principle is one of the most challenging principles of quantum theory, especially in the multi-particle situation. In the language of quantum mechanics, the high-order quantum interference of multi-particle is the consequence of a superposition among different yet indistinguishable probability amplitudes, a non-classical entity corresponding to different yet indistinguishable alternative ways of producing a joint-detection event among distant detectors. In optics, the theory of multiphoton interference of quantum light such as entangled photons are well established and accepted. On the other hand, classical interpretation is frequently used to explain the multiphoton interference of classical light such as thermal light and pseudo-thermal light due to the historical reasons. In this dissertation, we will focus on the study of high-order interference of photons in thermal and pseudo-thermal states. Sunlight, as a typical thermal light, contains a large number of independent and randomly radiated point subsources resulted from the spontaneous atomic transitions. The atomic transitions emit subfields at random positions and times with random phases. The pseudo-thermal light, consisting of a laser beam and a rotating diffusing ground glass, which is frequently used in the lab, can also be modeled as containing a large number of independent and randomly radiated subsouces. A large number of subelds with random phases are then generated from those subsources at random positions and times. As we will show in the dissertation, despite the classical feature of the source, the high-order interference of photons in thermal and pseudo-thermal states can only be fully understood by quantum theory due to the nonlocal nature. We gave a new analysis of the statistical property of pseudo-thermal light based on the coherent state representation following the Glauber-Scully theory. We showed that the new model can describe the energy distribution of the pseudo-thermal light very well. We then showed a novel detection scheme called Photon-Number Fluctuation Correlation(PNFC) protocol, which measures the photon number fluctuation of each of the photodetectors and calculates the statistical correlation between them. This scheme was then applied to measure a 100% HBT correlation and the result can be explained as a nonlocal two-photon interference phenomenon. In additional, the PNFC protocol can be applied to thermal light ghost imaging resulting a 100% visibility ghost imaging measurement as well as high resolution. A set of experiments on the foundations of quantum theory including the delayed-choice quantum eraser experiment and Popper's experiment are then discussed. Nonlocal interference of randomly paired photons measured with the PNFC protocol is applied to explain the experimental results. The single photon picture can lead to paradoxes that can only be understood with the nonlocal interference of random thermal photon pairs with themselves. The nonlocal feature in the interference of photons in thermal state then inspired us to simulate Bell sate with photons in thermal state and extended the test of Bell s inequality to the fluctuation correlation measurement. Experimental observation of Bell correlation from the polarization measurement of thermal fields in photon-number fluctuations is reported, the experimental test of Bell's inequality in photon-number fluctuations is also reported. We then extended this scheme to the simulation of 3-photon GHZ state. The successful simulation of n-photon entangled states can lead to new perspective for quantum computing with thermal light. To demonstrate the potential of thermal light quantum computing, a simulation of the controlled-NOT gate operation is shown in the last part of the thesis. Throughout the dissertation, we showed that the phenomena of photons in thermal and pseudo-thermal state can be more easily and deeply understood by quantum mechanics.
