Imagine you have a single beam of polarization-entangled photon pairs where photons of each pair have opposite polarization. This beam goes to a polarizing beam splitter. Of each pair, the vertical photon passes directly through and the horizontal photon is reflected 90 degrees left. After the beam splitter are to polarizing filters oriented at 40 degrees and anti-45 degrees relative to the axis of the beam splitter. Will the two photons of each pair either both pass the filters or not? This question boils down to whether the entanglement is broken by the beam splitter. I don't have a good reason why it should be broken. Now, imagine that after the BS on the vertical beam in a polarizer oriented vertically. All the photons reaching it should pass through. However, if on then place a polarizing filter oriented at 45 degrees in the horizontal beam, the polarization of those photons will be defined on the 45-degree axis. If photon pairs are still entangled, this would alter how many pass through the vertical filter. I conclude that I am stupid. Where is the flaw in my reasoning? It seems most likely that the beam splitter breaks the entanglement, but how does it do that?