(Note - I edited to the question in response to answers)
In the 1935 EPR paper, Einstein, Podolsky and Rosen write that given two entangled particles, one particle can be used to predict with certainty the value of a quantity of the second particle, or in other words the outcome of measurement on the second particle:
Thus, by measuring either A or B we are in a position to predict with certainty, and without in any way disturbing the second system, either the value of the quantity P or the value of the quantity Q.
One way to come to terms with this phenomenon is to stipulate faster than light interaction. This is how John Stewart Bell put it:
In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously, so that such a theory could not be Lorentz invariant.
However, if I understand correctly, the current view in physics is that the remote particles to not interact upon measurement, and the phenomena is viewed in terms of correlations.
In particular in Quantum Field Theory, which according to the Wikipedia "is brought forward as an unavoidable consequence of the reconciliation of quantum mechanics with special relativity", the remote particles do not interact. For example, see the following answer by the physicist Luboš Motl:
there are no interaction terms operating in between the two particles at all! Because there are no interactions, there is no influence, and the observed correlations clearly can't have anything to do with any non-local interactions.
So Einstein writes that the nearby particle can be used to predict with certainty the outcome of a measurement of the remote particle.
One can ask how the particle does it, and the answer is that we do not know.
Is it possible in principle to build a machine that can predict with certainty the outcome of a measurement on the remote particle?
The answer is yes, the machine could use the nearby particle as an "oracle" to make its prediction.
But is it possible in principle to build a machine that can predict with certainty the outcome of a measurement on the remote particle without using the nearby particle?
As far as we know, the answer is no.
In particular there is no (Turing) computation, not even in principle, that can make the prediction Einstein is writing about.
The question is therefore, why is quantum entanglement not acknowledged as an observable incomputable phenomenon?