A strong converse for classical channel coding using entangled inputs

TL;DR

This paper proves a strong converse for classical information transmission over quantum channels, showing that exceeding the capacity results in exponentially vanishing decoding success, even with entangled inputs, for many important quantum channels.

Contribution

It establishes a general strong converse for quantum channel coding using entangled inputs, extending previous results to a broad class of channels.

Findings

Strong converse holds for unital qubit channels

Valid for depolarizing and Werner-Holevo channels

Supports classical capacity as a sharp transmission threshold

Abstract

A fully general strong converse for channel coding states that when the rate of sending classical information exceeds the capacity of a quantum channel, the probability of correctly decoding goes to zero exponentially in the number of channel uses, even when we allow code states which are entangled across several uses of the channel. Such a statement was previously only known for classical channels and the quantum identity channel. By relating the problem to the additivity of minimum output entropies, we show that a strong converse holds for a large class of channels, including all unital qubit channels, the d-dimensional depolarizing channel and the Werner-Holevo channel. This further justifies the interpretation of the classical capacity as a sharp threshold for information-transmission.