  We define a large class of quantum sources and prove a quantum analog of the
asymptotic equipartition property. Our proof relies on using local measurements
on the quantum source to obtain an associated classical source. The classical
source provides an upper bound for the dimension of the relevant subspace of
the quantum source, via the Shannon-McMillan noiseless coding theorem. Along
the way we derive a bound for the von Neumann entropy of the quantum source in
terms of the Shannon entropy of the classical source, and we provide a
definition of ergodicity of the quantum source. Several explicit models of
quantum sources are also presented.
