Fig. 2. Pictorial illustration of propagation of conditional angle uncertainty.

(A) The cross section of the down-converted field as it propagates. For a line of idler positions, shown by green line, the signal photon has the probability of being found in the blue shaded region. The conditional angle uncertainty Δ(θ_s∣θ_i; z) is of the order of Δ(y_s∣y_i; z)/w_s(z), where Δ(y_s∣y_i; z) is the conditional position uncertainty of the signal photon and w_s(z) is the size of the down-converted field. (B) and (C) illustrate that the conditional angle uncertainty increases as a function of z in the near field, while in the far field, it decreases as a function of z.