  Interference of two photons at a beamsplitter is at the core of many quantum
photonic technologies, such as quantum key distribution or linear-optics
quantum computing. Observing high-visibility interference is challenging
because of the difficulty of realizing indistinguishable single-photon sources.
Here, we perform a two-photon interference experiment using phase-randomized
weak coherent states with different mean photon numbers. We place a tight upper
bound on the expected coincidences for the case when the incident wavepackets
contain single photons, allowing us to observe the Hong-Ou-Mandel effect. We
find that the interference visibility is at least as large as
0.995$^{+0.005}_{-0.013}$.
