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Conference Paper

Codes for Simultaneous Transmission of Quantum and Classical Information

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Grassl,  M.
Quantumness, Tomography, Entanglement, and Codes, Leuchs Division, Max Planck Institute for the Science of Light, Max Planck Society;

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Fulltext (public)

arXiv:1701.06963.pdf
(Preprint), 156KB

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Citation

Grassl, M., Lu, S., & Zeng, B. (in preparation). Codes for Simultaneous Transmission of Quantum and Classical Information.


Cite as: http://hdl.handle.net/21.11116/0000-0000-E389-5
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.