  The generation of ultrafast laser pulses and the reconstruction of their
electric fields is essential for many applications in modern optics. Quantum
optical fields can also be generated on ultrafast time scales, however, the
tools and methods available for strong laser pulses are not appropriate for
measuring the properties of weak, possibly entangled pulses. Here, we
demonstrate a method to reconstruct the joint-spectral amplitude of a
two-photon energy-time entangled state from joint measurements of the
frequencies and arrival times of the photons, and the correlations between
them. Our reconstruction method is based on a modified Gerchberg-Saxton
algorithm. Such techniques are essential to measure and control the shape of
ultrafast entangled photon pulses.
