  In the present paper we initiate the study of the product higher rank
numerical range. The latter, being a variant of the higher rank numerical range
[M.--D. Choi {\it et al.}, Rep. Math. Phys. {\bf 58}, 77 (2006); Lin. Alg.
Appl. {\bf 418}, 828 (2006)], is a natural tool for studying construction of
quantum error correction codes for multiple access channels. We review
properties of this set and relate it to other numerical ranges, which were
recently introduced in the literature. Further, the concept is applied to the
construction of codes for bi--unitary two--access channels with a hermitian
noise model. Analytical techniques for both outerbounding the product higher
rank numerical range and determining its exact shape are developed for this
case. Finally, the reverse problem of constructing a noise model for a given
product range is considered.
