Codes for Simultaneous Transmission of Quantum and Classical Information

Markus Grassl, Sirui Lu, Bei Zeng

Published 2017-01-24Version 1

We consider the characterization as well as the construction of quantum codes that allow to transmit both quantum and classical information, which we refer to as `hybrid codes'. We construct hybrid codes $[[n,k:m,d]]_q$ with length $n$ and distance $d$, that simultaneously transmit $k$ qudits and $m$ symbols from a classical alphabet of size $q$. Many good codes such as $[[7,1:1,3]]_2$, $[[9,2:2,3]]_2$, $[[10,3:2,3]]_2$, $[[11,1:2,4]]_2$ are found, with better parameters than hybrid codes obtained from the best known stabilizer quantum code. We also find a nonadditive $((11,2:20,3))_2$ code, with parameters beating the best known nonadditive quantum codes.