量子随机访问编码可恢复几乎全部原始信息，突破传统认知。
Getting almost all the bits from a quantum random access code
- 设计新测量方法，从量子态中提取接近完整信息
- 无论输入如何，都能以高概率恢复原串，误差小
- 适用于大尺寸编码，对研究量子信息压缩有启发
量子随机访问编码（QRAC）将n比特字符串映射为m量子比特的密度矩阵ρ_x，使得通过测量ρ_x能以成功率≥p恢复任意一个比特。传统方案中，恢复某一位会破坏其他位的信息，如2比特编码到1量子比特的情况。本文证明：这种“信息遮蔽”现象不会在大规模编码中持续存在。对于任意QRAC，均存在一种测量方式，可在高概率下恢复完整的n比特字符串，且与原串的汉明距离极小，即使在最坏情况下也成立。
原文摘要 · Abstract (English)
A quantum random access code (QRAC) is a map $x\mapstoρ_x$ that encodes $n$-bit strings $x$ into $m$-qubit quantum states $ρ_x$, in a way that allows us to recover any one bit of $x$ with success probability $\geq p$. The measurement on $ρ_x$ that is used to recover, say, $x_1$ may destroy all the information about the other bits; this is in fact what happens in the well-known QRAC that encodes $n=2$ bits into $m=1$ qubits. Does this generalize to large $n$, i.e., could there exist QRACs that are so "obfuscated" that one cannot get much more than one bit out of them? Here we show that this is not the case: for every QRAC there exists a measurement that (with high probability) recovers the full $n$-bit string $x$ up to small Hamming distance, even for the worst-case $x$.
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