Optimality of Meta-Converse for Channel Simulation

IEEE International Symposium on Information Theory (ISIT), pp. 1209–1214

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 exactly corresponds to the 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. As our main result, we prove a guarantee on the ratio of success probabilities of at least$(1-\frac{-1}{\mathbf{e}})$, for both the classical and the quantum setting. We further - show this ratio to be optimal. It can be improved to$(1-\frac{1}{t})$using$o$(ln$(t)$) additional bits (qubits) of communication.

Authors 3

1. Mario Berta Aachen Institute for Quantum Information

   RWTH Aachen University

   Affiliation as printed

   Institute for Quantum Information, RWTH Aachen University,Aachen,Germany

2. Omar Fawzi

   Lyon 1 Université · Institut national de recherche en sciences et technologies du numérique · École Normale Supérieure de Lyon · Laboratoire de l'Informatique du Parallélisme · QINFO: Traitement optimal de l'information avec des dispositifs quantiques

   Affiliation as printed

   Univ Lyon, Inria, ENS Lyon, UCBL, LIP.,Lyon,France

   QINFO - Traitement optimal de l'information avec des dispositifs quantiques (655 avenue de l'Europe 38334 Saint Ismier Cedex - France)

3. Aadil Oufkir Aachen Institute for Quantum Information

   RWTH Aachen University

   Affiliation as printed

   Institute for Quantum Information, RWTH Aachen University,Aachen,Germany