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The minimum number of photons necessary for activating the sense of vision has been a topic of research for over a century. The ability of rod cells to sense a few photons has implications for understanding the fundamental capabilities of the human visual and nervous system and creating new vision technologies based on photonics. We investigate the fundamental metrological capabilities of different quantum states of light to probe the retina, which is modeled using a simple neural network. Stimulating the rod cells by Fock, coherent and thermal states of light, and calculating the Cramer-Rao lower bound (CRLB) and Fisher information matrix for the signal produced by the ganglion cells in various conditions, we determine the volume of minimum error ellipsoid. Comparing the resulting ellipsoid volumes, we determine the metrological performance of different states of light for probing the retinal network. The results indicate that the thermal state yields the largest error ellipsoid volume and hence the worst metrological performance, and the Fock state yields the best performance for all parameters. This advantage persists even if another layer is added to the network or optical losses are considered in the calculations., Comment: 11 pages, 13 figures

Radical-pair reactions pertinent to biological magnetic field sensing are an ideal system for demonstrating the paradigm of quantum biology, the exploration of quantum coherene 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 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. Secondly, 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., 11 pages, 5 figures

Quantum vision is currently emerging as an interdisciplinary field synthesizing the physiology of human vision with modern quantum optics. We recently proposed a biometric scheme based on the human visual system's ability to perform photon counting. We here present a light stimulus source that can provide for the requirements of this biometric scheme, namely a laser light beam having a cross section consisting of discrete pixels, allowing for an arbitrary pattern of illuminated pixels, each having a photon number per unit time obeying a Poisson distribution around the mean. Both the illumination pattern and the photon number per pixel per unit time are computer controlled, offering simple and unsupervised scanning of these parameters. Moreover, infrared light exactly superimposed on the stimulus pattern can be used for acquiring exact information on the illumination geometry on the pupil. The same light stimulus source can be used to advance pupillometry to a higher level of control and precision, as current pupillometers lack spatial selectivity in illumination. We present pupillometry measurements demonstrating the potential of this source to offer a wealth of information on vision and brain function., 12 pages, 11 figures

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., 16 pages, 6 figures

It is known that the eye's scotopic photodetectors, rhodopsin molecules and their associated phototransduction mechanism leading to light perception, are efficient single photon counters. We here use the photon counting principles of human rod vision to propose a secure quantum biometric identification based on the quantum-statistical properties of retinal photon detection. The photon path along the human eye until its detection by rod cells is modeled as a filter having a specific transmission coefficient. Precisely determining its value from the photodetection statistics registered by the conscious observer is a quantum parameter estimation problem that leads to a quantum secure identification method. The probabilities for false positive and false negative identification of this biometric technique can readily approach $10^{-10}$ and $10^{-4}$, respectively. The security of the biometric method can be further quantified by the physics of quantum measurements. An impostor must be able to perform quantum thermometry and quantum magnetometry with energy resolution better than $10^{-9}\hbar$, in order to foil the device by non-invasively monitoring the biometric activity of a user., Comment: 16 pages, 4 figures

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 information, the quantum information extracted during the reaction, we reproduce the known and unravel other magnetic-field effects not conveyed by reaction yields., 8 pages, 3 figures

Chemically induced dynamic nuclear polarization is a ubiquitous phenomenon in photosynthetic reaction centers. The relevant nuclear spin observables are a direct manifestation of the radical-pair mechanism. We here use quantum trajectories to describe the time evolution of radical-pairs, and compare their prediction of nuclear spin observables to the one derived from the radical-pair master equation. While our approach provides a consistent description, we unravel a major inconsistency within the conven- tional theory, thus challenging the theoretical interpretation of numerous CIDNP experiments sensitive to radical-pair reaction kinetics., 7 pages, 3 figures

The radical-pair mechanism was introduced in the 1960's to explain anomalously large EPR and NMR signals in chemical reactions of organic molecules. It has evolved to the cornerstone of spin chemistry, the study of the effect electron and nuclear spins have on chemical reactions, with the avian magnetic compass mechanism and the photosynthetic reaction center dynamics being prominent biophysical manifestations of such effects. In recent years the radical-pair mechanism was shown to be an ideal biological system where the conceptual tools of quantum information science can be fruitfully applied. We will here review recent work making the case that the radical-pair mechanism is indeed a major driving force of the emerging field of quantum biology., Comment: 22 pages, 13 figures

Radical-ion-pair reactions, central in photosynthesis and the avian magnetic compass mechanism, have recently shown to be a paradigm system for applying quantum information science in a biochemical setting. The fundamental quantum master equation describing radical-ion-pair reactions is still under debate. We here use quantum retrodiction to produce a rigorous refinement of the theory put forward in Phys. Rev. E {\bf 83}, 056118 (2011). We also provide a rigorous analysis of the measure of singlet-triplet coherence required for deriving the radical-pair master equation. A Monte-Carlo simulation with single-molecule quantum trajectories supports the self-consistency of our approach., Comment: 12 pages, 8 figures

The radical-pair mechanism is understood to underlie the magnetic navigation capability of birds and possibly other species. Experiments with birds have provided indirect and in cases conflicting evidence on the actual existence of this mechanism. We here propose a new experiment that can unambiguously identify the presence of the radical-pair magnetoreceptor in birds and unravel some of its basic properties. The proposed experiment is based on modulated light excitation with a pulsed laser, combined with delayed radio-frequency magnetic field pulses. We predict a resonance effect in the birds' magnetic orientation versus the rf-pulse delay time. The resonance's position reflects the singlet-triplet mixing time of the magnetoreceptor., Comment: 5 pages, 5 figures

Chemically induced dynamic nuclear polarization is a signature of spin order appearing in many photosynthetic reaction centers. Such polarization, significantly enhanced above thermal equilibrium, is known to result from the nuclear spin sorting inherent in the radical pair mechanism underlying long-lived charge-separated states in photosynthetic reaction centers. We will here show that the recently understood fundamental quantum dynamics of radical-ion-pair reactions open up a new and completely unexpected venue towards obtaining CIDNP signals. The fundamental decoherence mechanism inherent in the recombination process of radical pairs is shown to produce nuclear spin polarizations on the order of $10^4$ times or more higher than the thermal equilibrium value at earth's magnetic field relevant to natural photosynthesis. This opens up the possibility of a fundamentally new exploration of the biological significance of high nuclear polarizations in photosynthesis., Comment: 7 pages, 4 figures

Radical-ion pairs, fundamental for understanding photosynthesis and the avian magnetic compass, were recently shown to be biological open quantum systems. We here show that the coupling of the radical-pair's spin degrees of freedom to its decohering vibrational reservoir leads to a shift of the radical-pair's magnetic energy levels. The Lamb shift Hamiltonian is diagonal in the singlet-triplet basis, and results in a singlet-triplet energy splitting physically indistinguishable from an exchange interaction. This could have significant implications for understanding the energy level structure and the dynamics of photosynthetic reaction centers., Comment: 7 pages, 2 figures

We investigate the physical meaning of quantum superposition states between reactants and products in electron transfer reactions. We show that such superpositions are strongly suppressed and to leading orders of perturbation theory do not pertain in electron transfer reactions. This is because of the intermediate manifold of states separating the reactants from the products. We provide an intuitive description of these considerations with Feynman diagrams. We also discuss the relation of such quantum coherences to understanding the fundamental quantum dynamics of spin-selective radical-ion-pair reactions., 4 pages, 5 figures

We present the quantum limits to the magnetic sensitivity of a new kind of magnetometer based on biochemical reactions. Radical-ion-pair reactions, the biochemical system underlying the chemical compass, are shown to offer a new and unique physical realization of a magnetic field sensor competitive to modern atomic or condensed matter magnetometers. We elaborate on the quantum coherence and entanglement dynamics of this sensor, showing that they provide the physical basis for testing our understanding of the fundamental quantum dynamics of radical-ion-pair reactions., 5 pages, 2 figures

It is shown that the Jones-Hore theory is either inconsistent or cannot describe single-molecule experiments., 1 page

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 propose a concrete experimental test that can clearly discriminate among the fundamental master equations currently attempting to describe the quantum dynamics of these reactions. The proposed measurement based on photon statistics of fluorescing radical pairs is shown to be model-independent and capable of elucidating the singlet-triplet decoherence inherent in the radical-ion-pair recombination process., Comment: 4 pages, 2 figures

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., 9 pages, 5 figures, published version

Magnetic-sensitive radical-ion-pair reactions are understood to underlie the biochemical magnetic compass used by avian species for navigation. Recent experiments have provided growing evidence for the radical-ion-pair magnetoreception mechanism, while recent theoretical advances have unravelled the quantum nature of radical-ion-pair reactions, which were shown to manifest a host of quantum-information-science concepts and effects, like quantum measurement, quantum jumps and the quantum Zeno effect. We here show that the quantum Zeno effect provides for the robustness of the avian compass mechanism, and immunizes it's magnetic and angular sensitivity against the deleterious and molecule-specific exchange and dipolar interactions., Comment: 6 pages, 4 figures

Chemical reactions involving radical-ion pairs are ubiquitous in biology, since not only are they at the basis of the photosynthetic reaction chain, but are also assumed to underlie the biochemical magnetic compass used by avian species for navigation. Recent experiments with magnetic-sensitive radical-ion pair reactions provided strong evidence for the radical-ion-pair magnetoreception mechanism, verifying the expected magnetic sensitivities and chemical product yield changes. It is here shown that the theoretical description of radical-ion-pair reactions used since the 70's cannot explain the observed data, because it is based on phenomenological equations masking quantum coherence effects. The fundamental density matrix equation derived here from basic quantum measurement theory considerations naturally incorporates the quantum Zeno effect and readily explains recent experimental observations on low- and high-magnetic-field radical-ion-pair reactions., 10 pages, 5 figures