固定多通量子传感中每吸收光子的通用损耗限制最优值
A universal loss-limited optimum for fixed multi-pass quantum sensing per absorbed photon
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中文总结 AI 辅助
本研究针对样本稀缺场景下的多通量子传感，推导得出由单个常数确定的所有固定单光子多通方案的损耗限制最优值，验证了其在多个传感问题中的普适性，发现单个循环光子是脆弱样本的最优测量方式。
中文摘要 AI 辅助
多通方案让光子多次穿过样本以获取更多样本信息。当样本而非光较为稀缺时，天然的品质因数是物体每吸收一个光子所获得的信息。我们证明，存在一个常数确定了所有固定方案的损耗限制最优值——这类方案中单个光子反复穿过样本并在末端被检测一次。三个性质足以支撑该结论：信息随通过次数的平方增长、每次通过的存活概率固定，以及已损失的光子不会产生剂量。这些性质推导出唯一的权衡函数$h(x)=x^2/(e^x-1)$，其中$x$为通过次数乘以每次通过的损耗。该函数的最大值为0.648，出现在$x_{\text{opt}}=1.594$处。无相互作用询问的损耗限制上限与Yu等人提出的多通相位最优值是两个实例。弱吸收物体的相位传感是第三个实例，其最优通过次数为$m_{\text{opt}}=x_{\text{opt}}/(ε+α)$；吸收系数$α$和寄生损耗$ε$仅通过二者之和影响最优值，但损伤仅由$α$决定。N00N态及其抗损耗推广形式在每吸收光子的信息获取上表现更差，同时优化光子数和通过次数会得到单个循环光子的结果。另外两个问题也可用同一度量衡量。对于吸收估计，任何方案都无法获得增益。检测瑞利极限以下的微弱伴星时，伴星承受的剂量与其微弱程度无关，而直接成像下剂量会无限制增长。对于脆弱样本，最温和的测量也是最简单的：单个循环光子。
英文摘要
Multi-pass schemes send a photon through a sample several times to learn more about it. When the sample rather than the light is scarce, the natural figure of merit is the information gained per photon the object absorbs. We show that one constant fixes the loss-limited optimum of every fixed scheme in which a single photon passes repeatedly through the sample and is detected once at the end. Three properties suffice: information that grows as the square of the pass number, a fixed survival probability per pass, and no dose from a photon already lost. They force a single trade-off function $h(x)=x^2/(e^x-1)$, where $x$ is the number of passes times the loss per pass. Its maximum, 0.648, sits at $x_{\mathrm{opt}}=1.594$. The loss-limited ceiling of interaction-free interrogation and the multi-pass phase optimum of Yu et al. are two instances. Phase sensing of a weakly absorbing object is a third, optimal at $m_{\mathrm{opt}}=x_{\mathrm{opt}}/(ε+α)$ passes; the absorption $α$ and the parasitic loss $ε$ enter the optimum only through their sum, but the damage counts only $α$. N00N states and their loss-robust generalisations do worse per absorbed photon, and optimising over photon number and pass number together returns a single recycled photon. Two further problems are priced in the same measure. Absorption estimation gains nothing, for any scheme. Detecting a faint companion below the Rayleigh limit costs the companion a dose that does not depend on its faintness, while under direct imaging the dose grows without bound. For a fragile sample the gentlest measurement is also the simplest one: a single photon, recycled.
