  We present the construction of standard entanglement-assisted (EA) qubit
Reed-Muller (RM) codes and their tensor product variants from classical RM
codes. We show that the EA RM codes obtained using the CSS construction have
zero coding rate and negative catalytic rate. We further show that EA codes
constructed from these same classical RM codes using the tensor product code
(TPC) construction have positive coding rate and provide a subclass of EA RM
TPCs that have positive catalytic rate, thus establishing the coding analog of
superadditivity for this family of codes, useful towards quantum
communications. We also generalize this analysis to obtain conditions for EA
TPCs from classical codes to have positive catalytic rate when their
corresponding EA CSS codes have zero rate.
