If Father Christmas behaves as a quantum entity (a santon, presumably
with very large charm and quantum numbers), physics allows him to pass
through many orifices (chimneys) at the same time.
This is possible as long as no experiment is set up to observe him
passing through any particular chimney (otherwise his wave function
collapses and you end up with reindeer all over the place).
All children are told that they must never attempt to detect santons,
so the success of the scheme is a great tribute to the obedience of the
children of the world; for this to work they must all be good.
After Father Christmas has passed through all the chimneys at once it
is permissible to detect the santon field on a suitable detector. It
would seem that santons are detected by pine trees and stockings, which
register the collapse of the santon field as small piles of presents.
The fact that presents never appear in stockings already occupied by a
foot may be a consequence of the Pauli Exclusion Principle.
Thus Father Christmas can visit all the children in the world at the
same time and can continue to do so as long as we never attempt to
observe him passing through a particular chimney. I strongly suggest
that funding for experiments to do this should be withheld as success
would mean no presents.