  It is shown that a classical optical Fourier processor can be used for the
shaping of quantum correlations between two or more photons, and the class of
Fourier masks applicable in the multiphoton Fourier space is identified. This
concept is experimentally demonstrated using two types of periodic phase masks
illuminated with path-entangled photon pairs, a highly non-classical state of
light. Applied first were sinusoidal phase masks, emulating two-particle
quantum walk on a periodic lattice, yielding intricate correlation patterns
with various spatial bunching and anti-bunching effects depending on the
initial state. Then, a periodic Zernike-like filter was applied on top of the
sinusoidal phase masks. Using this filter, phase information lost in the
original correlation measurements was retrieved.
