局部可解码代码将n位串x编码为m位码字C（x），以这样的方式，即可以通过仅查询该字的几位来从损坏的码字中恢复任何位x_i。我们使用量子论证来证明具有2个经典查询的LDCs需要指数长度：m=2^{Omega（n）}。以前，这只适用于线性码（Goldreich et al. 02）。我们的证明表明，一个2查询LDC可以解码只有1个量子查询，然后证明了指数下界，这样的1查询局部量子可解码的代码。我们还表明，q量子查询允许更简洁的最不发达国家比最有名的最不发达国家与q经典查询。最后，我们给出了新的经典下界和量子上界的设置私人信息检索。特别是，我们展示了一个量子2-服务器PIR方案，具有O（n^{3/10}）量子比特的通信，改进了最著名的经典2-服务器PIR的O（n^{1/3}）比特的通信。
英文摘要：
A locally decodable code encodes n-bit strings x in m-bit codewords C(x), in such a way that one can recover any bit x_i from a corrupted codeword by querying only a few bits of that word. We use a quantum argument to prove that LDCs with 2 classical queries need exponential length: m=2^{Omega(n)}. Previously this was known only for linear codes (Goldreich et al. 02). Our proof shows that a 2-query LDC can be decoded with only 1 quantum query, and then proves an exponential lower bound for such 1-query locally quantum-decodable codes. We also show that q quantum queries allow more succinct LDCs than the best known LDCs with q classical queries. Finally, we give new classical lower bounds and quantum upper bounds for the setting of private information retrieval. In particular, we exhibit a quantum 2-server PIR scheme with O(n^{3/10}) qubits of communication, improving upon the O(n^{1/3}) bits of communication of the best known classical 2-server PIR.
Optimal query complexity for fractional quantum evolution
National University of Singapore（新加坡国立大学）；Royal Holloway University of London（伦敦皇家霍洛威学院）；University of Oxford（牛津大学）；Nanyang Technological University（南洋理工大学）
Tight bounds for hybrid quantum-classical query algorithms
Center for Quantum Computer Science, Faculty of Computing, University of Latvia（拉脱维亚大学计算学院量子计算机科学中心）；Alfréd Rényi Institute of Mathematics, Budapest, Hungary（阿尔弗雷德·雷尼数学研究所）
