  Strong correlations in two conjugate variables are the signature of quantum
entanglement and have played a key role in the development of modern physics.
Entangled photons have become a standard tool in quantum information and
foundations. An impressive example is position-momentum entanglement of photon
pairs, explained heuristically through the correlations implied by a common
birth zone and momentum conservation. However, these arguments entirely neglect
the importance of the `quantumness', i.e. coherence, of the driving force
behind the generation mechanism. We study theoretically and experimentally how
the correlations depend on the coherence of the pump of nonlinear
down-conversion. In the extreme case - a truly incoherent pump - only position
correlations exist. By increasing the pump's coherence, correlations in momenta
emerge until their strength is sufficient to produce entanglement. Our results
shed light on entanglement generation and can be applied to adjust the
entanglement for quantum information applications.
