Quantum channels show exact secrecy limits for private communication

The exact strong converse exponent for private communication over quantum channels

Information Theory

Summary

Sending secret messages through quantum channels can be tricky because eavesdroppers might listen in. This paper finds the exact rate at which the chance of keeping messages secret drops sharply if you try to send information faster than the channel’s private capacity. The authors introduce a new way to measure privacy that helps them describe this drop precisely. Their findings prove that if you exceed the private capacity, the reliability of secret communication fails at an exponential pace.

What this means in practice

A theory result. No direct application yet.

Authors

Hao-Chung Cheng, Christoph Hirche, Marco Tomamichel

Abstract

We determine the exact strong converse exponent for secret-key transmission and generation over general finite-dimensional quantum wiretap channels, measuring reliability and secrecy jointly by squared fidelity to an ideal secret key. We introduce a novel Renyi private information whose regularization characterizes this exponent. An exact integral representation in terms of ordinary private information gives a uniform continuity bound, showing that the regularized quantity converges to private capacity as the Renyi order approaches one. This establishes for any wiretap channel an exponential fidelity decay at every rate above private capacity.