10.4230/LIPIcs.STACS.2009.1813
Briet, Jop
de Wolf, Ronald
Locally Decodable Quantum Codes
Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH, Wadern/Saarbruecken, Germany
2009
Computer Science
000 Computer science, knowledge, general works
Herbstritt, Marc
2009-02-19
eng
ConferencePaper
12 pages
application/pdf
1.0
Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license (CC-BY-NC-ND)
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 $q$.