when quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2009.1813
URN: urn:nbn:de:0030-drops-18134
URL: http://drops.dagstuhl.de/opus/volltexte/2009/1813/

Briet, Jop ; de Wolf, Ronald

### Locally Decodable Quantum Codes

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### Abstract

We study a quantum analogue of locally decodable error-correcting codes. A $q$-query \emph{locally decodable quantum code} encodes $n$ classical bits in an $m$-qubit state, in such a way that each of the encoded bits can be recovered with high probability by a measurement on at most $q$ qubits of the quantum code, even if a constant fraction of its qubits have been corrupted adversarially. We show that such a quantum code can be transformed into a \emph{classical} $q$-query locally decodable code of the same length that can be decoded well on average (albeit with smaller success probability and noise-tolerance). This shows, roughly speaking, that $q$-query quantum codes are not significantly better than $q$-query classical codes, at least for constant or small $q$.

### BibTeX - Entry

@InProceedings{briet_et_al:LIPIcs:2009:1813,
author =	{Jop Briet and Ronald de Wolf},
title =	{{Locally Decodable Quantum Codes}},
booktitle =	{26th International Symposium on Theoretical Aspects of Computer Science},
pages =	{219--230},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-939897-09-5},
ISSN =	{1868-8969},
year =	{2009},
volume =	{3},
editor =	{Susanne Albers and Jean-Yves Marion},
publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},