Title: Channel simulation: tight meta converse for error and strong converse exponents
Speaker: Michael Xuan Cao（RWTH Aachen University）
Time: 07.31 (Thursday), 10:00-11:00
Venue: Gewu Building 315
Abstract:We determine the exact error and strong converse exponents of shared randomness-assisted channel simulation in worst case total-variation distance. Namely, we find that these exponents can be written as simple optimizations over the Rényi channel mutual information. Strikingly, and in stark contrast to channel coding, there are no critical rates, allowing a tight characterization for arbitrary rates below and above the simulation capacity. We derive our results by asymptotically expanding the meta-converse for channel simulation [Cao et al., IEEE Trans. Inf. Theory (2024)], which corresponds to non-signaling assisted codes. We prove this to be asymptotically tight by employing the approximation algorithms from [Berta et al., Proc. IEEE ISIT (2024)], which show how to round any non-signaling assisted strategy to a strategy that only uses shared randomness. Notably, this implies that any additional quantum entanglement-assistance does not change the error or the strong converse exponents.
