发表机构
Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area（粤港澳大湾区量子科学中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出利用量子参考实现无需经典描述的泄漏检测，证明相干测量方案在零误报下具有指数级样本优势，远超经典测量优先方法。
AI 中文摘要
已知编码子空间的泄漏可以通过投影来检测。然而，当编码子空间未被经典指定时，相应的投影算子不可用。这里我们展示了由同一编码器制备的独立量子参考如何在没有编码的经典描述的情况下实现泄漏检测。对参考和单个消息进行相干测量，使得二维编码子空间内的每个状态（包括其与远程系统的纠缠）完全保持不变。我们推导了 $M$ 个理想参考的精确检测定律，并证明了在每次编码的零误报测试中的最优性。对于正交泄漏，漏检概率渐近于 $4/M$，与环境维度 $d$ 无关。先测量所有参考（即使是集体测量），在相同的零误报要求下，在任何有限预算下检测为零。对于介于零和一之间的固定检测目标，在正常误报和条件扰动的足够小容差 $\epsilon$ 下，最优的测量优先成本为 $\Theta(d/\epsilon)$；而一个与维度无关的相干预算就足够了。对于编码在三个物理量子位中的一个逻辑量子位，七个相干参考可实现至少 $50\\%$ 的正交泄漏检测，而在相同的 $1\\%$ 正常容差下，任何测量优先接收器至少需要 $588$ 个参考。因此，量子参考支持无需经典重构的泄漏检查，其样本优势随物理量子位数指数增长。
英文摘要
Leakage from a known encoding subspace can be detected by projection. However, the corresponding projector is unavailable when the encoding subspace is not classically specified. Here we show how independent quantum references prepared by the same encoder enable leakage detection without a classical description of the encoding. A coherent measurement on the references and a single message leaves every state within the two-dimensional encoding subspace, including its entanglement with a remote system, exactly unchanged. We derive the exact detection law for $M$ ideal references and prove optimality among tests with zero false alarm for every encoding. For orthogonal leakage, the miss probability is asymptotic to $4/M$, independent of the ambient dimension $d$. Measuring all references first, even collectively, gives zero detection at every finite budget under the same zero-false-alarm requirement. For a fixed detection target between zero and one, the optimal measurement-first cost is $Θ(d/ε)$ at sufficiently small tolerance $ε$ on normal false alarm and conditional disturbance; a dimension-independent coherent budget suffices. For one logical qubit encoded in three physical qubits, seven coherent references achieve at least $50\%$ orthogonal-leakage detection, whereas any measurement-first receiver needs at least $588$ under the same $1\%$ normal tolerances. Quantum references thus support leakage checks without classical reconstruction, with a sample advantage exponential in the number of physical qubits.
Comments25 pages, 4 figures; Supplemental Material included
