Codes for Simultaneous Transmission of Quantum and Classical Information

Markus Grassl; Sirui Lu; Bei Zeng

doi:10.1109/ISIT.2017.8006823

paper

Codes for Simultaneous Transmission of Quantum and Classical Information

arXiv:1701.06963 · doi:10.1109/ISIT.2017.8006823

Abstract

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 $[[7, 1 : 1, 3]]_{2}$ , $[[9, 2 : 2, 3]]_{2}$ , $[[10, 3 : 2, 3]]_{2}$ , $[[11, 4 : 2, 3]]_{2}$ , $[[11, 1 : 2, 4]]_{2}$ , $[[13, 1 : 4, 4]]_{2}$ , $[[13, 1 : 1, 5]]_{2}$ , $[[14, 1 : 2, 5]]_{2}$ , $[[15, 1 : 3, 5]]_{2}$ , $[[19, 9 : 1, 4]]_{2}$ , $[[20, 9 : 2, 4]]_{2}$ , $[[21, 9 : 3, 4]]_{2}$ , $[[22, 9 : 4, 4]]_{2}$ have been found. All these codes have better parameters than hybrid codes obtained from the best known stabilizer quantum codes.

6 pages

Codes for Simultaneous Transmission of Quantum and Classical Information

Abstract

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