Both beam splitters are modelled as the unitary matrix B = 1 2 ( 1 i i 1 ) , which means that when a photon meets the beam splitter it will either stay on the same path with a probability amplitude of 1 / 2 , or be reflected to the other path with a probability amplitude of i / 2 . The phase shifter on the upper arm is modelled as the unitary matrix P = ( 1 0 0 e i Δ Δ Φ Φ ) , which means that if the photon is on the "upper" path it will gain a relative phase of Δ Δ Φ Φ , and it will stay unchanged if it is in the lower path.