Random coding exponents galore via decoupling

TL;DR

This paper establishes quantum coding exponents for various quantum information protocols by deriving exponential bounds on decoupling errors using Rnyi information measures, advancing the theoretical understanding of quantum communication efficiency.

Contribution

It provides the first comprehensive derivation of random coding exponents for multiple quantum information-processing protocols using decoupling techniques.

Findings

Exponential bounds on decoupling errors for quantum protocols

Application of Rnyi b5-information measures in exponent calculations

Extension to protocols like quantum state merging and broadcast channels

Abstract

A missing piece in quantum information theory, with very few exceptions, has been to provide the random coding exponents for quantum information-processing protocols. We remedy the situation by providing these exponents for a variety of protocols including those at the top of the family tree of protocols. Our line of attack is to provide an exponential bound on the decoupling error for a restricted class of completely positive maps where a key term in the exponent is in terms of a R\'enyi \alpha-information-theoretic quantity for any \alpha $\in$ (1,2]. Among the protocols covered are fully quantum Slepian-Wolf, quantum state merging, quantum state redistribution, quantum/classical communication across channels with side information at the transmitter with or without entanglement assistance, and quantum communication across broadcast channels.