Quantum channel coding: Approximation algorithms and strong converse exponents

arXiv (Cornell University)

Abstract

We study relaxations of entanglement-assisted quantum channel coding and establish that non-signaling assistance and a natural semi-definite programming relaxation\, -- \,termed meta-converse\, -- \,are equivalent in terms of success probabilities. We then present a rounding procedure that transforms any non-signaling-assisted strategy into an entanglement-assisted one and prove an approximation ratio of $(1 - e^{-1})$ in success probabilities for the special case of measurement channels. For fully quantum channels, we give a weaker (dimension dependent) approximation ratio, that is nevertheless still tight to characterize the strong converse exponent of entanglement-assisted channel coding [Li and Yao, IEEE Tran.~Inf.~Theory (2024)]. Our derivations leverage ideas from position-based coding, quantum decoupling theorems, the matrix Chernoff inequality, and input flattening techniques.

Authors 2

1. Aadil Oufkir Aachen Institute for Quantum Information

   RWTH Aachen University · Université Mohammed VI Polytechnique

   Affiliation as printed

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

   The UM6P Vanguard Center , Mohammed VI Polytechnic University , Rocade Rabat-Salé , Technopolis , Morocco

2. Mario Berta Aachen Institute for Quantum Information

   RWTH Aachen University

   Affiliation as printed

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