Radical-pair reactions pertinent to biological magnetic field sensing are an ideal system for demonstrating the paradigm of quantum biology, the exploration of quantum coherence effects in complex biological systems.We here provide yet another fundamental connection between this biochemical spin system and quantum information science.We introduce and explore a formal measure quantifying the singlet-triplet coherence of radical pairs using the concept of quantum relative entropy.The ability to quantify singlet-triplet coherence opens up a number of possibilities in the study of magnetic sensing with radical pairs.We first use the explicit quantification of singlet-triplet coherence to affirmatively address the major premise of quantum biology, namely, that quantum coherence provides an operational advantage to magnetoreception.Second, we use the concept of incoherent operations to show that incoherent manipulations of nuclear spins can have a dire effect on singlet-triplet coherence when the radical pair exhibits electronic-nuclear entanglement.Finally, we unravel subtle effects related to exchange interactions and their role in promoting quantum coherence.
Radical-pair reactions pertinent to biological magnetic field sensing are an ideal system for demonstrating the paradigm of quantum biology, the exploration of quantum coherence effects in complex biological systems.We here provide yet another fundamental connection between this biochemical spin system and quantum information science.We introduce and explore a formal measure quantifying the singlet-triplet coherence of radical pairs using the concept of quantum relative entropy.The ability to quantify singlet-triplet coherence opens up a number of possibilities in the study of magnetic sensing with radical pairs.We first use the explicit quantification of singlet-triplet coherence to affirmatively address the major premise of quantum biology, namely, that quantum coherence provides an operational advantage to magnetoreception.Second, we use the concept of incoherent operations to show that incoherent manipulations of nuclear spins can have a dire effect on singlet-triplet coherence when the radical pair exhibits electronic-nuclear entanglement.Finally, we unravel subtle effects related to exchange interactions and their role in promoting quantum coherence.
Abstract A fundamental concept of quantum physics, the Wigner–Yanase information, is used here as a measure of quantum coherence in spin‐dependent radical‐pair reactions pertaining to biological magnetic sensing. This measure is connected to the uncertainty of the reaction yields and, further, to the statistics of a cellular receptor‐ligand system used to biochemically convey magnetic‐field changes. Measurable physiological quantities, such as the number of receptors and fluctuations in ligand concentration, are shown to reflect the introduced Wigner–Yanase measure of singlet‐triplet coherence. A quantum‐biological uncertainty relation connecting the product of a biological resource and a biological figure of merit with the Wigner–Yanase coherence is arrived at. This approach can serve as a general search for quantum‐coherent effects within cellular environments.
Radical-ion-pair reactions, central for understanding the avian magnetic compass and spin transport in photosynthetic reaction centers, were recently shown to be a fruitful paradigm of the new synthesis of quantum information science with biological processes. We here show that the master equation so far constituting the theoretical foundation of spin chemistry violates fundamental bounds for the entropy of quantum systems, in particular the Ozawa bound. In contrast, a recently developed theory based on quantum measurements, quantum coherence measures and quantum retrodiction, thus exemplifying the paradigm of quantum biology, satisfies the Ozawa bound as well as the Lanford-Robinson bound on information extraction. By considering Groenewold's information, the quantum information extracted during the reaction, we reproduce the known and unravel new magnetic-field effects not conveyed by reaction yields.
Radical-ion-pair reactions, central for understanding the avian magnetic compass and spin transport in photosynthetic reaction centers, were recently shown to be a fruitful paradigm of the new synthesis of quantum information science with biological processes. We show here that the master equation so far constituting the theoretical foundation of spin chemistry violates fundamental bounds for the entropy of quantum systems, in particular the Ozawa bound. In contrast, a recently developed theory based on quantum measurements, quantum coherence measures, and quantum retrodiction, thus exemplifying the paradigm of quantum biology, satisfies the Ozawa bound as well as the Lanford-Robinson bound on information extraction. By considering Groenewold's information, the quantum information extracted during the reaction, we reproduce the known and unravel other magnetic-field effects not conveyed by reaction yields.
The development of the radical pair mechanism has allowed for theoretical explanation of the fact that magnetic fields are observed to have an effect on chemical reactions. The mechanism describes how an external magnetic field can alter chemical yields by interacting with the spin state of a pair of radicals. In the field of quantum biology, there has been some interest in the application of the mechanism to biological systems. This paper takes an open quantum systems approach to a model of the radical pair mechanism in order to derive a master equation in the Born-Markov approximation for the case of two electrons, each interacting with an environment of nuclear spins as well as the external magnetic field, then placed in a dissipative bosonic bath. This model is used to investigate two different cases relating to radical pair dynamics. The first uses a collective coupling approach to simplify calculations for larger numbers of nuclei interacting with the radical pair. The second looks at the effects of different hyperfine configurations of the radical pair model, for instance the case in which one of the electrons interact with two nuclei with different hyperfine coupling constants. The results of these investigations are analysed to see if they offer any insights into the biological application of the radical pair mechanism in avian magnetoreception.
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.
Electron spin-dependent chemical reactions in proteins, often discussed under the 'radical-pair mechanism', remain the leading microscopic proposal for magnetic field sensing in biology. Yet the essential physics is often obscured by the complexity of realistic models. In this work, we present a physicist-friendly primer on the simplest radical-pair Hamiltonian that already captures many of the mechanism's best-known qualitative features. The contributions of this work are fourfold. First, we place on record a complete analytical solution of this toy model, which has previously been studied extensively, mostly through numerical and partial analytical approaches. Working in the experimentally relevant singlet-triplet basis, we derive closed-form expressions for the instantaneous singlet population and for two related time-averaged singlet yields. Second, we introduce a new interpretation of these results that makes several familiar features of radical-pair physics transparent. In particular, we show that the dynamics admit a bright-dark decomposition (in the sense of spin mixing), similar to structures studied in atomic physics. Third, through this bright-dark perspective, we clarify experimentally relevant features of the toy model. In particular, we show that the so-called 'low-field effect' arises from a coherence term between bright and dark sectors, and that the special role of zero field is best understood as a phase-locking phenomenon rather than merely as enhanced mixing. Fourth, we import methods developed in the context of technological quantum sensing to obtain further insight into the model. This allows us to clarify the role of initial state preparation and the trade-off between coherent phase accumulation and time-averaging penalties. The resulting toy model serves both as an analytically tractable benchmark and as a conceptual starting point for future work.