Locally Decodable Quantum Codes

Authors Jop Briet, Ronald de Wolf

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Jop Briet
Ronald de Wolf

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Jop Briet and Ronald de Wolf. Locally Decodable Quantum Codes. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 219-230, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)


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 $q$.
  • Data structures
  • Locally decodable codes
  • Quantum computing


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