Optimality of meta-converse for channel simulation - Archive ouverte HAL
Communication Dans Un Congrès Année : 2024

Optimality of meta-converse for channel simulation

Résumé

We study the effect of shared non-signaling correlations for the problem of simulating a channel using noiseless communication in the one-shot setting. For classical channels, we show how to round any non-signaling-assisted simulation strategy--which corresponds to the natural linear programming meta-converse for channel simulation--to a strategy that only uses shared randomness. For quantum channels, we round any non-signaling-assisted simulation strategy to a strategy that only uses shared entanglement. Our main result is for classical and classical-quantum channels, for which we employ ideas from approximation algorithms to give a guarantee on the ratio of success probabilities of at least $(1-\mathrm{e}^{-1})$. We further show this ratio to be optimal for the purely classical case. It can be improved to $(1-t^{-1})$ using $O(\ln \ln(t))$ additional bits of communication.

Dates et versions

hal-04824978 , version 1 (07-12-2024)

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Mario Berta, Omar Fawzi, Aadil Oufkir. Optimality of meta-converse for channel simulation. ISIT 2024 - IEEE International Symposium on Information Theory, Jul 2024, Athens, Greece. pp.1209-1214, ⟨10.1109/ISIT57864.2024.10619187⟩. ⟨hal-04824978⟩
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