AI 中文总结
研究具有密度算子编码和任意解码测量的量子随机访问码是否遵循推测界，发现含私有随机性的经典随机访问码违反该界，通过特定构造产生反例，有限块长度分析得出量子比特缩放结论，确定经典编码率为分离来源并推动受限界发展。
AI 中文摘要
我们考虑每个具有密度算子编码和任意解码测量的量子随机访问码（QRAC）是否遵循推测的界$p\leq(1+\sqrt{m/n})/2$，其中$n$个经典比特被编码为$m$个量子比特，$p$是最坏情况成功概率。我们发现具有私有随机性的经典随机访问码违反了该界，将这些经典码嵌入为具有对角编码态和对易解码测量的QRAC，并构造具有相同解码统计的纯态实现。Ambainis等人的可达性定理在足够大的输入长度下对每个固定的$p\in(1/2,1)$产生违反情况。反例跨越了每个固定压缩率下推测界和Nayak界之间的整个开区间。有限块长度分析进一步得出，对于恢复偏差按$\sqrt{\log_2 n/n}$缩放且具有足够大前置因子的情况，量子比特缩放具有阶最优对数缩放。这些结果确定了经典编码率是分离的来源，并基于解码测量的定量谱特性推动了受限界的发展。
英文摘要
We consider whether every quantum random access code (QRAC) with density-operator encodings and arbitrary decoding measurements obeys the conjectured bound $p\leq(1+\sqrt{m/n})/2$, where $n$ classical bits are encoded into $m$ qubits and $p$ is the worst-case success probability. We find that classical random access codes with private randomness, which form a subclass of this QRAC model, violate the bound. We embed these classical codes as QRACs with diagonal encoding states and commuting decoding measurements, and construct pure-state realizations with identical decoding statistics. The achievability theorem of Ambainis, Nayak, Ta-Shma, and Vazirani then yields violations for every fixed $p\in(1/2,1)$ at sufficiently large input length. The counterexamples span the full open interval between the conjectured and Nayak bounds at each fixed compression rate. A finite-blocklength analysis further yields order-optimal logarithmic qubit scaling for a recovery bias scaling as $\sqrt{\log_2 n/n}$ with a sufficiently large prefactor. These results identify the classical coding rate as the source of the separation and motivate restricted bounds based on quantitative spectral properties of decoding measurements.
Comments17 pages, 1 figure, 1 table
