Quantum Theory of Two-Photon Wavepacket Interference in a Beam Splitter

We study a general theory on the interference of a two-photon wavepacket in a beam splitter. The theory is carried out in the Schr\"{o}dinger picture so that the quantum nature of the two-photon interference is explicitly presented. We find that the topological symmetry of the probability-amplitude spectrum of the two-photon wavepacket dominates the manners of two-photon interference which are distinguished according to increasing and decreasing the coincidence probability for the absence of interference. However, two-photon entanglement can be witnessed by the interference manner. We demonstrate the necessary and sufficient conditions for the perfect two-photon interference. For a two-photon entangled state with an anti-symmetric spectrum, it passes a 50/50 beam splitter with the perfect transparency. The theory contributes an unified understanding to a variety of the two-photon interference effects.