It is known that the "unbounded quantum fanout operation" is very powerful: (See, for example, Hoyer et al. : http://theoryofcomputing.org/articles/v001a005/v001a005.pdf).
In particular, it is known that many operations that cannot be done in constant depth classical circuits can be done in constant depth quantum cicuits that include the quantum fan-out operation.
However, I can't seem to find any discussion as to whether "constant depth" fanout is possible physically.
In classical computation, it seems fairly reasonable to consider "fan-out" to be an operation that does not add to the "depth" of a circuit: such a computational model models the latency of actual physical circuits of reasonable size.
For a fair comparison, unbounded quantum fanout would need to be achievable using some kind of experiment with a latency that scales as a constant with the size of the fanout (if it scales even logarithmically, then that kind of defeats the whole advantage of the quantum fanout operation).
Is there any experimental evidence to suggest whether such constant-latency quantum fanout unitary operations are feasible?