Optimality of meta-converse for channel simulation

TL;DR

This paper investigates the optimality of the meta-converse approach in channel simulation, demonstrating how non-signaling strategies can be approximated by shared randomness or entanglement, with proven success probability guarantees.

Contribution

It establishes that non-signaling-assisted strategies can be rounded to simpler shared resources with optimal success guarantees for classical and quantum channels.

Findings

The ratio of success probabilities is at least (1 - e^{-1}) for classical and classical-quantum channels.

This ratio is proven to be optimal in the classical case.

The ratio can be improved to (1 - 1/t) with additional communication.

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.