Coalescence and Anti-Coalescence Interference of Two-Photon Wavepacket in a Beam Splitter

We study theoretically the interference of a two-photon wavepacket in a beam splitter. We find that the spectrum symmetry for the two-photon wavepacket dominates the perfect coalescence and anti-coalescence interference. The coalescence interference is unrelated to photon entanglement. Only the anti-coalescence interference has evidence of photon entanglement. We prove that the two-photon wavepacket with an anti-symmetric spectrum is transparent to pass the 50/50 beam splitter, showing perfect anti-coalescence interference.