On the undecidability of quantum channel capacities
Archishna Bhattacharyya (University of Ottawa)
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.
This is based on arXiv 2601.22471 — joint work with Arthur Mehta and Yuming Zhao.
Location
QNC 3206
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