局部可解码量子码
Locally Decodable Quantum Codes
摘要：
我们研究了一种局部可解码纠错码的量子模拟。q查询可局部解码的量子码在m量子比特状态中编码n个经典比特，使得每个编码比特可以通过对量子码的至多q个量子比特的测量以高概率恢复，即使其量子比特的恒定部分已经被反向破坏。我们表明，这样的量子代码可以转换成一个经典的q查询本地解码代码的相同长度，可以解码以及平均（虽然具有较小的成功概率和噪声容忍度）。这表明，粗略地说，q-查询量子码并不比q-查询经典码好，至少对于常数或小q。
英文摘要：
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.
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