Optimality of meta-converse for channel simulation

Aadil Oufkir; Omar Fawzi; Mario Berta

doi:10.1109/isit57864.2024.10619187

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arXiv · 2410.08140

Optimality of meta-converse for channel simulation

Aadil Oufkir·Omar Fawzi·Mario Berta

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Abstract

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.

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Aadil Oufkir, Omar Fawzi, Mario Berta. 2024-10-10. Optimality of meta-converse for channel simulation. https://doi.org/10.1109/isit57864.2024.10619187

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