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arXiv:2301.11023 · Advanced Quantum Technologies

Physiological Search for Quantum Biological Sensing Effects Based on the Wigner–Yanase Connection between Coherence and Uncertainty

Iannis K. Kominis

Published Nov 16, 2023• 5 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1002/qute.202300292

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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-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-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.
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 were recently shown to represent a rich biophysical laboratory for the application of quantum measurement theory methods and concepts. We here show that radical-ion-pair reactions essentially form a non-linear biochemical double slit interferometer. Quantum coherence effects are visible when which-path information is limited, and the incoherent limit is approached when measurement-induced decoherence sets in. Based on this analogy with the optical double slit experiment we derive and elaborate on the fundamental master equation of spin-selective radical-ion-pair reactions that covers the continuous range from complete incoherence to maximum singlet-triplet coherence.
Abstract Wigner–Yanase skew information could quantify the quantum uncertainty of the observables that are not commuting with a conserved quantity. We present the uncertainty principle for two successive projective measurements in terms of Wigner–Yanase skew information based on a single quantum system. It could capture the incompatibility of the observables, i.e. the lower bound can be nontrivial for the observables that are incompatible with the state of the quantum system. Furthermore, the lower bound is also constrained by the quantum Fisher information. In addition, we find the complementarity relation between the uncertainties of the observable which operated on the quantum state and the other observable that performed on the post-measured quantum state and the uncertainties formed by the non-degenerate quantum observables performed on the quantum state, respectively.
The Wigner-Araki-Yanase theorem puts a limitation on the measurement of observables in the presence of a conserved quantity, and the notion of Wigner-Yanase skew information quantifies the amount of information on the values of observables not commuting with the conserved quantity. We demonstrate that the statistical idea underlying the skew information is the Fisher information in the theory of statistical estimation. A quantum Cramér-Rao inequality and a new uncertainty relation in terms of the skew information are established, which shed considerable new light on the relationships between quantum measurement and statistical inference. The result is applied to estimating the evolution speed of quantum states.