Strong converse rates for quantum communication

TL;DR

This paper proves that for quantum channels, exceeding the Rains information rate leads to exponentially vanishing fidelity, establishing a strong converse property for quantum communication, especially over generalized dephasing channels.

Contribution

It demonstrates that the Rains information is a strong converse rate for quantum communication, even with classical post-processing, and confirms this for generalized dephasing channels.

Findings

Rains information is a strong converse rate for quantum channels.

Fidelity decays exponentially if rate exceeds Rains information.

Strong converse property established for generalized dephasing channels.

Abstract

We revisit a fundamental open problem in quantum information theory, namely whether it is possible to transmit quantum information at a rate exceeding the channel capacity if we allow for a non-vanishing probability of decoding error. Here we establish that the Rains information of any quantum channel is a strong converse rate for quantum communication: For any sequence of codes with rate exceeding the Rains information of the channel, we show that the fidelity vanishes exponentially fast as the number of channel uses increases. This remains true even if we consider codes that perform classical post-processing on the transmitted quantum data. As an application of this result, for generalized dephasing channels we show that the Rains information is also achievable, and thereby establish the strong converse property for quantum communication over such channels. Thus we conclusively settle the strong converse question for a class of quantum channels that have a non-trivial quantum capacity.