Fundamental bound on the reliability of quantum information transmission

TL;DR

This paper establishes a fundamental bound on the reliability of quantum information transmission, demonstrating that above the quantum channel capacity, reliability decays exponentially, similar to classical channels.

Contribution

It provides the first explicit bound on the reliability decay for quantum information transmission above capacity, extending classical information theory results to quantum channels.

Findings

Reliability decays exponentially above quantum channel capacity.

First explicit bound on quantum information transmission reliability.

Framework for generalized reliability bounds.

Abstract

Information theory tells us that if the rate of sending information across a noisy channel were above the capacity of that channel, then the transmission would necessarily be unreliable. For classical information sent over classical or quantum channels, one could, under certain conditions, make a stronger statement that the reliability of the transmission shall decay exponentially to zero with the number of channel uses and the proof of this statement typically relies on a certain fundamental bound on the reliability of the transmission. Such a statement or the bound has never been given for sending quantum information. We give this bound and then use it to give the first example where the reliability of sending quantum information at rates above the capacity decays exponentially to zero. We also show that our framework can be used for proving generalized bounds on the reliability.