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DOI: 10.4230/LIPIcs.STACS.2009.1813
URN: urn:nbn:de:0030-drops-18134
URL: https://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},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2009/1813},
URN = {urn:nbn:de:0030-drops-18134},
doi = {10.4230/LIPIcs.STACS.2009.1813},
annote = {Keywords: Data structures, Locally decodable codes, Quantum computing}
}
| Keywords: | Data structures, Locally decodable codes, Quantum computing | |
| Seminar: | 26th International Symposium on Theoretical Aspects of Computer Science | |
| Issue date: | 2009 | |
| Date of publication: | 19.02.2009 |
