Codes for Simultaneous Transmission of Quantum and Classical Information
Grassl, M., Lu, S., Zeng, B. · MPG.PuRe (Max Planck Society) · 2017
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.