Before the measurement the positions of the photons in space are not defined, thus the distance between them also makes no sense and without distance one cannot really speak about the speed of information transfer. So IMO finding the properties of two entangled photons correlated is no more and no less surprising than finding the exact position of just one photon: the particle that was kind of “spread out all over space” before the measurement suddenly and instantaneously (basically “with infinite speed”, if one can dare to define a notion of “speed” in this case) “gathers itself together” in one particular spot. That what quantum mechanics is all about.

Yurii Pidopryhora (14. 08. 2008), [[http://www.nature.com/news/2008/080813/full/news.2008.1038.html]]