  We introduce and initiate the study of a family of higher rank matricial
ranges, taking motivation from hybrid classical and quantum error correction
coding theory and its operator algebra framework. In particular, for a noisy
quantum channel, a hybrid quantum error correcting code exists if and only if a
distinguished special case of the joint higher rank matricial range of the
error operators of the channel is non-empty. We establish bounds on Hilbert
space dimension in terms of properties of a tuple of operators that guarantee a
matricial range is non-empty, and hence additionally guarantee the existence of
hybrid codes for a given quantum channel. We also discuss when hybrid codes can
have advantages over quantum codes and present a number of examples.
