Quantum sensing enables the ultimate precision attainable in parameter estimation. Circumstantial evidence suggests that certain organisms, most notably migratory songbirds, also harness quantum-enhanced magnetic field sensing via a radical-pair-based chemical compass for the precise detection of the weak geomagnetic field. However, what underpins the acuity of such a compass operating in a noisy biological setting, at physiological temperatures, remains an open question. Here, we address the fundamental limits of inferring geomagnetic field directions from radical-pair spin dynamics. Specifically, we compare the compass precision, as derived from the directional dependence of the radical-pair recombination yield, to the ultimate precision potentially realisable by a quantum measurement on the spin system under steady-state conditions. To this end, we probe the quantum Fisher information and associated Cramér–Rao bound in spin models of realistic complexity, accounting for complex inter-radical interactions, a multitude of hyperfine couplings, and asymmetric recombination kinetics, as characteristic for the magnetosensory protein cryptochrome. We compare several models implicated in cryptochrome magnetoreception and unveil their optimality through the precision of measurements ostensibly accessible to nature. Overall, the comparison provides insight into processes honed by nature to realise optimality whilst constrained to operating with mere reaction yields. Generally, the inference of compass orientation from recombination yields approaches optimality in the limits of complexity, yet levels off short of the theoretical optimal precision bounds by up to one or two orders of magnitude, thus underscoring the potential for improving on design principles inherent to natural systems.

中文翻译：

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论自由基对量子罗盘的最优性


量子传感使参数估计能够达到最高的精度。间接证据表明，某些生物体，尤其是迁徙鸣禽，也通过基于自由基对的化学罗盘利用量子增强磁场传感来精确检测微弱的地磁场。然而，是什么支撑着这种指南针在嘈杂的生物环境和生理温度下运行的敏锐度，仍然是一个悬而未决的问题。在这里，我们解决了从自由基对自旋动力学推断地磁场方向的基本限制。具体来说，我们将罗盘精度（源自自由基对复合产率的方向依赖性）与稳态条件下自旋系统的量子测量可能实现的最终精度进行比较。为此，我们探讨了量子费希尔信息和相关的克拉梅-拉奥束缚在现实复杂性的自旋模型中，解释了复杂的自由基间相互作用、大量超精细耦合和不对称重组动力学，作为磁感应蛋白隐花色素的特征。我们比较了与隐花磁接收有关的几种模型，并通过表面上可用于自然界的测量精度揭示了它们的最优性。总体而言，这种比较提供了对自然磨练的过程的深入了解，以实现最优性，同时仅限于仅以反应产率进行操作。 一般来说，从重组中推断罗盘方向在复杂性的限度内接近最优，但与理论上的最佳精度界限相差一两个数量级，从而强调了改进自然固有设计原理的潜力。系统。