On the undecidability of quantum channel capacities

Archishna Bhattacharyya; Arthur Mehta; Yuming Zhao

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arXiv · 2601.22471

On the undecidability of quantum channel capacities

Archishna Bhattacharyya·Arthur Mehta·Yuming Zhao

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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 entanglement-assisted zero-error capacity under some restrictions is uncomputable; indicative of the fact that quantum channel capacities may generally be undecidable.

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Archishna Bhattacharyya, Arthur Mehta, Yuming Zhao. 2026-01-30. On the undecidability of quantum channel capacities. https://arxiv.org/abs/2601.22471

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