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  1. ; ; (, Communications in Mathematical Physics)
    Abstract A finite groupGis calledC-quasirandom (by Gowers) if all non-trivial irreducible complex representations ofGhave dimension at leastC. For any unit$$\ell ^{2}$$ ℓ 2 function on a finite group we associate thequantum probability measureon the group given by the absolute value squared of the function. We show that if a group is highly quasirandom, in the above sense, then any Cayley graph of this group has an orthonormal eigenbasis of the adjacency operator such that the quantum probability measures of the eigenfunctions put close to the correct proportion of their mass on suitably selected subsets of the group that are not too small. 
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