Both beam splitters are modelled as the unitary matrix formula_116, which means that when a photon meets the beam splitter it will either stay on the same path with a probability amplitude of formula_117, or be reflected to the other path with a probability amplitude of formula_118. The phase shifter on the upper arm is modelled as the unitary matrix formula_119, which means that if the photon is on the "upper" path it will gain a relative phase of formula_120, and it will stay unchanged if it is in the lower path.