%0 Journal Article
%T A characterization of freeness by invariance under quantum spreading
%A Stephen Curran
%J Mathematics
%D 2010
%I arXiv
%X We construct spaces of quantum increasing sequences, which give quantum families of maps in the sense of Soltan. We then introduce a notion of quantum spreadability for a sequence of noncommutative random variables, by requiring their joint distribution to be invariant under taking quantum subsequences. Our main result is a free analogue of a theorem of Ryll-Nardzewski: for an infinite sequence of noncommutative random variables, quantum spreadability is equivalent to free independence and identical distribution with respect to a conditional expectation.
%U http://arxiv.org/abs/1002.4390v2