Quantum-limited biochemical magnetometers designed using the Fisher information and quantum reaction control

Abstract

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. 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 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. arXiv:1611.08902v1 [quant-ph]

Navigating at night: fundamental limits on the sensitivity of radical pair magnetoreception under dim light

“…Use of the data processing inequality (Nielsen and Chuang, 2010; Beaudry and Renner, 2011) leads to a lower bound estimate of the precision with which a bird could orient itself using only the geomagnetic field as a directional cue (Section ‘Lower bound error in the head direction’). This approach avoids the difficulty faced by a simpler Fisher information treatment (Lehmann and Casella, 1998; Guo et al ., 2017; Vitalis and Kominis, 2017) which cannot account for arbitrary signal processing. We then estimate the photon flux into model cryptochrome-containing cells within the retina under the dim light conditions experienced by night-migratory songbirds (Section ‘Magnetoreceptor cells’) and assess the achievability of the information theory lower bound using a simple parameterised model of the singlet yield and two elementary data-processing approaches (Section ‘A model radical pair’).…”

Quantum Biometrics with Retinal Photon Counting

“…Part of the recent quest to explore the possibilities biological systems offer for novel quantum technology realizations [11][12][13] has been the question of how well biological photodetectors, in particular rhodopsin molecules in retinal rod cells [14], compare with modern photodetectors [15]. Historically, the role of photon statistics in vision was addressed in the 1930's [16] and elucidated with human behavioral experiments in the 1940's [17][18][19], single cell responses have been recorded since the 1970's [20][21][22][23][24], while it was only recently that the quantum physics of human vision [25] was addressed with the modern experimental [26][27][28][29][30] and theoretical [31][32][33][34] tools of quantum optics.…”

Quantum relative entropy shows singlet-triplet coherence is a resource in the radical-pair mechanism of biological magnetic sensing

“…Moreover, quantum information concepts like violation of entropy bounds were taken advantage of to further demonstrate [17] the inadequacy of the long-standing theoretical foundations of spin chemistry [18] in a general way unaffected by the precise knowledge, or lack thereof, of molecular parameters. Most recently, quantum metrology methods were introduced to study the fundamental limits to quantum sensing of magnetic fields using radical-pair reactions and treating them as biochemical quantum magnetometers [19].…”