Magnetosensitive spin-correlated radical pairs offer a promising platform for noise-robust quantum metrology; however, unavoidable interradical interactions, such as electron-electron dipolar and exchange couplings, alongside deleterious perturbations resulting from intrinsic radical motion, typically degrade their potential as magnetometers. In contrast, we show how structured molecular motion modulating interradical interactions in a chemical sensor in cryptochrome can, in fact, increase sensitivity and, moreover, push precision in estimating magnetic field directions closer to the quantum Cramér-Rao bound. The latter is evident both on average over the magnetoreceptor array and, to an even greater extent, for the subset of best-performing magnetoreceptors, thus suggesting near-optimal metrological performance. Remarkably, this approach to optimality is amplified under environmental noise and persists with increasing complexity of the spin system, suggesting that perturbations inherent to such natural systems have enabled them to operate closer to the quantum limit to more effectively extract information from the weak geomagnetic field. This insight opens the possibility of channeling the underlying physical principles of motion-induced modulation of electron spin-spin interactions toward devising efficient handles over emerging molecular quantum information technologies.
Magnetosensitive spin-correlated radical pairs offer a promising platform for noise-robust quantum metrology; however, unavoidable interradical interactions, such as electron-electron dipolar and exchange couplings, alongside deleterious perturbations resulting from intrinsic radical motion, typically degrade their potential as magnetometers. In contrast, we show how structured molecular motion modulating interradical interactions in a chemical sensor in cryptochrome can, in fact, increase sensitivity and, moreover, push precision in estimating magnetic field directions closer to the quantum Cramér-Rao bound. The latter is evident both on average over the magnetoreceptor array and, to an even greater extent, for the subset of best-performing magnetoreceptors, thus suggesting near-optimal metrological performance. Remarkably, this approach to optimality is amplified under environmental noise and persists with increasing complexity of the spin system, suggesting that perturbations inherent to such natural systems have enabled them to operate closer to the quantum limit to more effectively extract information from the weak geomagnetic field. This insight opens the possibility of channeling the underlying physical principles of motion-induced modulation of electron spin-spin interactions toward devising efficient handles over emerging molecular quantum information technologies.
The quantum control of spin-correlated radical pairs (SCRPs) holds promise for the targeted manipulation of magnetic field effects (MFEs), with potential applications ranging from the design of noise-resilient quantum information processors to genetically encodable quantum sensors. However, achieving precise handles over the intricate interplay between coherent electron spin dynamics and incoherent relaxation processes in photo-excited radical-pair reactions requires tractable approaches for numerically obtaining controls for large, complex open quantum systems. To that end, we realise optimal control of SCRPs in the low-magnetic-field regime, through first generalising the gradient-ascent pulse engineering (GRAPE) paradigm to allow for optimising time-integral reaction yields for coherent control of SCRP spin dynamics. We then explore how interradical interactions which are unavoidable in a biophysical setting, such as electron-electron dipolar and exchange couplings, alongside driving resulting from intrinsic structural motion, can push the precision of the proposed radical pair quantum compass in cryptochrome closer to approaching the quantum Cram\'{e}r-Rao bound. Remarkably, this approach to optimality is amplified under environmental noise and persists with increasing complexity of the spin system, suggesting that perturbations inherent to such natural systems have enabled them to operate closer to the quantum limit to more effectively extract information from the weak geomagnetic field. Bolstered by these findings, we furthermore demonstrate how a control engineering approach based on the Pontryagin Maximum Principle (PMP) can offer a more computationally feasible route towards realising not only coherent, but also incoherent control, of noisy SCRP open-system spin dynamics. This raises prospects for experimental realisation of spin control of actual radical-pair systems in ambient magnetic fields, by suppressing or boosting radical reaction yields using purpose-specific radio-frequency wave forms, paving the way for inspiring more noise-robust quantum magnetometry via chemical reaction-yield-dependence, and potentially applications of quantum control to physiologically relevant radical-pair reaction intermediates.
Abstract 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.
Radical-ion pairs and their reactions have triggered the study of quantum effects in biological systems. This is because they exhibit a number of effects best understood within quantum information science, and at the same time are central in understanding the avian magnetic compass and the spin transport dynamics in photosynthetic reaction centers. Here we address radical-pair reactions from the perspective of quantum metrology. Since the coherent spin motion of radical pairs is effected by an external magnetic field, these spin-dependent reactions essentially realize a biochemical magnetometer. Using the quantum Fisher information, we find the fundamental quantum limits to the magnetic sensitivity of radical-pair magnetometers, arriving at a sensitivity $\ensuremath{\delta}B=2\phantom{\rule{0.16em}{0ex}}\mathrm{pT}/\ensuremath{\tau}[1\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\text{s}]\sqrt{{\ensuremath{\nu}}_{0}[{10}^{12}]}$, given in terms of radical-pair lifetime $\ensuremath{\tau}$ and number of radical pairs ${\ensuremath{\nu}}_{0}$. We then explore how well the usual measurement scheme considered in radical-pair reactions, the measurement of reaction yields, approaches the fundamental limits. In doing so, we find the optimal hyperfine interaction Hamiltonian that leads to the best magnetic sensitivity as obtained from reaction yields. This is still an order of magnitude smaller than the absolute quantum limit. Finally, we demonstrate that with a realistic quantum reaction control reminding one of Ramsey interferometry, here presented as a quantum circuit involving the spin-exchange interaction and a recently proposed molecular switch, we can approach the fundamental quantum limit within a factor of 2. This work opens the application of well-advanced quantum metrology methods to biological systems.
The quantum control of spin-correlated radical pairs may enable the targeted manipulation of magnetic field effects, with potential long-term applications across molecular quantum technologies, from prospective noise-resilient quantum information processors to genetically encodable quantum sensors. However, achieving precise handles over the intricate interplay between coherent electron spin dynamics and incoherent relaxation processes in photoexcited radical-pair reactions requires tractable approaches for numerically obtaining controls for large, complex open quantum systems. Employing techniques relying on full Liouville-space propagators to that end becomes computationally infeasible for large spin systems of realistic complexity. Here, we demonstrate how a control engineering approach based on the Pontryagin Maximum Principle (PMP) can offer a viable alternative by reporting on the successful application of PMP-optimal control to steer the coherent and incoherent spin dynamics of noisy radical pairs. This enables controls for prototypical radical-pair models that exhibit robustness in the face of relevant noise sources and paves the way to incoherent control of radical-pair spin dynamics.
Abstract Avian magnetoreception based on the radical-pair mechanism explains how migratory birds navigate using the geomagnetic field. However, how these microscopic quantum states persist against environmental noise in vivo remains a fundamental challenge. We address this by presenting a scalable vectorized state-space framework of open quantum dynamics under decoherence, universally applicable to arbitrary n-particle spin-coupled systems. By vectorizing the density matrix in the Lindblad master equation, we map the spin dynamics from Hilbert to Liouville space, bypassing traditional numerical bottlenecks. Crucially, leveraging initial singlet-state constraints reduces the active decoherence operators from 64 to 16, significantly accelerating open-system simulations. Projecting triplet yields onto a virtual retina model reveals that environmental noise exerts dual, pathway-dependent effects on navigation accuracy. While singlet–singlet relaxation (SS) and longitudinal phase dephasing (ST0) degrade sensitivity through contrast washout, transverse phase dephasing (ST±) acts counterintuitively as a "quantum lens". This transverse channel filters off-axis noise, concentrating triplet yields at the retinal center to enhance magnetic sensitivity by 35.2%. These findings demonstrate that environmental noise can be constructively harnessed, offering a new design paradigm for noise-tolerant, high-precision bionic quantum compasses.
Practical performance of quantum sensors is often curtailed by uncontrolled environmental drift (bias-field instability, temperature fluctuations, mechanical vibration), background fields, and imperfect control pulses. This motivates developing physical mechanisms that intrinsically compensate for such perturbations while retaining high sensitivity to target fields. We introduce an interaction-protected magnetometry scheme where periodic driving steers the collective magnetization onto two long-lived, prethermal Floquet "orbit" axes well-separated on the Bloch sphere. Rapid toggling between these axes encodes target fields as a differential signal, whereas background fields appear as common-mode motion that is strongly rejected, achieving >1000-fold suppression while canceling prethermal transients. This enables accurate reconstruction of rapidly varying audio-band magnetic signals without predictive filtering or spectral tuning. We provide an experimental proof-of-principle using a dense ensemble of coupled nuclear spins, operated here as a broadband (0-1 kHz) magnetometer. The protocol is remarkably tolerant to imperfections, operating robustly across millions of pulses under pulse-angle (~10°) and pulse frequency (>1 kHz) errors, large bias-field drifts (>50 μT), temperature variations over 150 K, and harsh mechanical vibrations. These results establish Floquet prethermalization as a resource for robust quantum sensors that combines broadband magnetic-field sensitivity with intrinsic immunity to diverse environmental and control perturbations, opening a path toward stable quantum metrology beyond controlled laboratory conditions.