On the undecidability of quantum channel capacities

Archishna Bhattacharyya, Arthur Mehta, Yuming Zhao (Feb 02 2026).

Abstract: An important distinction in our understanding of capacities of classical versus quantum channels is marked by the following question: is there an algorithm which can compute (or even efficiently compute) the capacity? While there is overwhelming evidence suggesting that quantum channel capacities may be uncomputable, a formal proof of any such statement is elusive. We initiate the study of the hardness of computing quantum channel capacities. We show that, for a general quantum channel, it is QMA-hard to compute its quantum capacity, and that the maximal-entanglement-assisted zero-error one-shot classical capacity is uncomputable.

Arxiv: https://arxiv.org/abs/2601.22471