  We study a quantum analogue of locally decodable error-correcting codes. A
q-query 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 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.
