  The problem of channel coding over the Gaussian multiple-input
multiple-output (MIMO) broadcast channel (BC) with additive independent
Gaussian states is considered. The states are known in a noncausal manner to
the encoder, and it wishes to minimize the amount of information that the
receivers can learn from the channel outputs about the state sequence. The
state leakage rate is measured as a normalized blockwise mutual information
between the state sequence and the channel outputs' sequences. We employ a new
version of a state-dependent extremal inequality and show that Gaussian input
maximizes the state-dependent version of Marton's outer bound. Further we show
that our inner bound coincides with the outer bound. Our result generalizes
previously studied scalar Gaussian BC with state and MIMO BC without state.
