  We construct high order low-bit Sigma-Delta $(\Sigma \Delta)$ quantizers for
the vector-valued setting of fusion frames. We prove that these $\Sigma \Delta$
quantizers can be stably implemented to quantize fusion frame measurements on
subspaces $W_n$ using $\log_2( {\rm dim}(W_n)+1)$ bits per measurement. Signal
reconstruction is performed using a version of Sobolev duals for fusion frames,
and numerical experiments are given to validate the overall performance.
