QED by Richard Feynman
Recently, I was reminded of the difference between hearing someone and reading someone, so I grabbed this Feynmnan lecture set. Instrumentally, the best part was seeing the rigor required to pull apart some of these problems. I don't see this enough in daily life, so I'm probably doing something wrong.
The complete story on this situation is very interesting: if the detectors at A and B are not perfect, and detect photons only some of the time, then there are three distinguishable final conditions...
As the reliability of the detectors increases, we get less interference.