There is a dispute on PhysicsForums related to what are the conditions necessary for two photons to be entangled by a beam splitter. Lots of references given by the forum users but they never arrive at the same conclusions. https://www.physicsforums.com/threads/quantum-entanglement-by-the-means-of-beam-splitters.852464/
Must they already be part of entangled pairs and does the beam splitter just swap the entanglement between the members of the different pairs? Can the beam splitter be used alone to entangle photons or can it entangle them only in the presence of many other elements like polarizers, wave plates, prisms, dichroic mirrors? Can the input photons be distinguishable or must they always be indistinguishable?