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Locally Decodable Quantum Codes

Abstract : We study a quantum analogue of locally decodable error-correcting codes. A q-query local ly 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 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.
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https://hal.inria.fr/inria-00359198
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Submitted on : Friday, February 6, 2009 - 11:50:11 AM
Last modification on : Wednesday, December 20, 2017 - 5:42:07 PM
Long-term archiving on: : Tuesday, June 8, 2010 - 7:12:13 PM

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  • HAL Id : inria-00359198, version 1
  • ARXIV : 0806.2101

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Jop Briët, Ronald de Wolf. Locally Decodable Quantum Codes. 26th International Symposium on Theoretical Aspects of Computer Science STACS 2009, Feb 2009, Freiburg, Germany. pp.219-230. ⟨inria-00359198⟩

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