# Codes for Simultaneous Transmission of Quantum and Classical Information

## TL;DR

This paper introduces hybrid quantum-classical codes that enable simultaneous transmission of quantum and classical information, demonstrating constructions with superior parameters compared to existing stabilizer codes.

## Contribution

The authors construct new hybrid codes with explicit parameters, improving upon the best known stabilizer quantum codes for combined quantum and classical data transmission.

## Key findings

- Constructed hybrid codes with various parameters such as $[ exttt{[}7,1{: }1,3 exttt{]}]_2$ and $[ exttt{[}22,9{: }4,4 exttt{]}]_2$.
- Hybrid codes outperform existing stabilizer codes in transmitting both quantum and classical information.
- Provided explicit examples of hybrid codes with better parameters than known quantum codes.

## 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.