Quantum在线内存检查
Quantum Online Memory Checking
摘要：
内存检查的问题考虑将文件存储在不可靠的公共服务器上，其内存可能被恶意方修改。主要任务是设计一个在线内存检查器，能够验证服务器上的信息没有被损坏。为了存储n位公共信息，内存校验器有s个私有可靠位用于校验目的;而为了检索每一位公共信息，校验器与公共内存通信t位。早期的研究表明，对于经典的记忆检查器，s*t \in Ω（n）的下限成立。在这篇文章中，我们研究量子内存检查器，有s个私人量子比特，并允许量子查询公共内存使用t个量子比特。我们证明了一个指数级的改进，通过显示量子检查器的存在，使用量子指纹，只需要s \in O（log n）量子位的本地存储器和t \in O（polylog n）量子位的通信与公共存储器。
英文摘要：
The problem of memory checking considers storing files on an unreliable public server whose memory can be modified by a malicious party. The main task is to design an online memory checker with the capability to verify that the information on the server has not been corrupted. To store n bits of public information, the memory checker has s private reliable bits for verification purpose; while to retrieve each bit of public information the checker communicates t bits with the public memory. Earlier work showed that, for classical memory checkers, the lower bound s*t \in Omega(n) holds. In this article we study quantum memory checkers that have s private qubits and that are allowed to quantum query the public memory using t qubits. We prove an exponential improvement over the classical setting by showing the existence of a quantum checker that, using quantum fingerprints, requires only s \in O(log n) qubits of local memory and t \in O(polylog n) qubits of communication with the public memory.
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