Quantum channel coding: Approximation algorithms and strong converse exponents

Quantum, vol. 9, pp. 1877

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