On the Additivity Conjecture in Quantum Information Theory

A class of problems in quantum information theory, which have elementary formulations but still resist solutions, concerns the additivity properties (with respect to tensor products of channels) of various quantities characterizing quantum channels such as the “classical capacity” or “maximal output purity.” All known results, including extensive numerical work, are consistent with this conjecture. A proof of this conjecture would have important consequences in quantum information theory. In particular, according to this conjecture, the classical capacity or the maximal purity of outputs cannot be increased by using entangled inputs of the channel. In this paper, we state some additivity/multiplicativity problems, give relations between them, and prove some new partial results, which also support the conjecture.