Dephrasure channel and superadditivity of coherent information

TL;DR

This paper investigates the dephrasure channel, revealing its complex properties like nonadditivity of coherent information and positive quantum capacity, which are crucial for understanding quantum communication limits.

Contribution

It introduces the dephrasure channel as a simple yet rich model to study nonadditivity and quantum capacity in quantum information theory.

Findings

Nonadditivity of coherent information at two-letter level

Large gap between single-letter coherent and private informations

Positive quantum capacity for all complementary channels

Abstract

The quantum capacity of a quantum channel captures its capability for noiseless quantum communication. It lies at the heart of quantum information theory. Unfortunately, our poor understanding of nonadditivity of coherent information makes it hard to understand the quantum capacity of all but very special channels. In this paper, we consider the dephrasure channel, which is the concatenation of a dephasing channel and an erasure channel. This very simple channel displays remarkably rich and exotic properties: we find nonadditivity of coherent information at the two-letter level, a big gap between single-letter coherent and private informations, and positive quantum capacity for all complementary channels. Its clean form simplifies the evaluation of coherent information substantially and, as such, we hope that the dephrasure channel will provide a much-needed laboratory for the testing of new ideas about nonadditivity.