更好的短种子量子防护提取器
Better short-seed quantum-proof extractors
摘要：
我们构造了一个针对量子存储的强提取器，该提取器适用于每个最小熵$k$，具有对数种子长度，并输出$Ω(k)$位，前提是量子对手对于任何$β< \half$最多具有$βk$量子位的存储器。这种构造的工作原理是首先压缩源（具有最小的熵损失），然后应用一个提取器，当源接近均匀时，该提取器可以很好地对抗量子对手。我们还得到了一个改进的强量子证明提取器在高最小熵制度的建设。具体来说，我们构建了一个提取器，使用对数种子长度和提取$Ω(n)$位从任何源在$\B^n$，只要源的最小熵条件下的量子对手的状态至少是$(1-β) n$，对于任何$β< \half$。
英文摘要：
We construct a strong extractor against quantum storage that works for every min-entropy $k$, has logarithmic seed length, and outputs $Ω(k)$ bits, provided that the quantum adversary has at most $βk$ qubits of memory, for any $β< \half$. The construction works by first condensing the source (with minimal entropy-loss) and then applying an extractor that works well against quantum adversaries when the source is close to uniform. We also obtain an improved construction of a strong quantum-proof extractor in the high min-entropy regime. Specifically, we construct an extractor that uses a logarithmic seed length and extracts $Ω(n)$ bits from any source over $\B^n$, provided that the min-entropy of the source conditioned on the quantum adversary's state is at least $(1-β) n$, for any $β< \half$.
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