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arXiv:1010.1495

Comment on "Quantum Control and Entanglement in a Chemical Compass"

Iannis K. Kominis

Published Oct 7, 2010• 0 citations
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Abstract

In this comment we show that the avian compass entanglement considerations of J. Cai, G. G. Guerreschi and H. J. Briegel (Phys. Rev. Lett. 104, 220502 (2010)) result in unphysical predictions on the magnetic sensitivity of this biochemical sensor. As well known from a series of papers on precision measurements and detailed derivations of standard quantum limits, not taking into account decoherence results in an overestimate of the entanglement lifetime, and this is the case at hand. The entanglement lifetime is wrongly assumed by the authors to be independent of the reaction time (the inverse of the recombination rate) and hence it is grossly overestimated. This is so because the spin coherence lifetime is limited by the reaction time, and the entanglement lifetime cannot be any longer.

DOI
10.48550/arxiv.1010.1495

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In a recent paper, cond-mat/0405331 (Ref. 1), del Barco et al. reported experimental studies on a Ni4 molecular system. They used an experimental method (combining microwave spectroscopy with high sensitivity magnetic measurements) that we have introduced before, cond-mat/0404410 (see also Ref. 2 and 3). Among other things, our technique allows us to monitor spin-state populations in the presence of microwave magnetic fields. Absorption line-widths give rough 'upper bounds' on the decoherence rate similar to 'standard' high frequency electron paramagnetic resonance (HF-EPR) techniques. In the case of quasi continuous radiation our technique does NOT give directly the spin-lattice relaxation time T1. For measurements like those of del Barco et al., it simply gives access to the phonon-bottleneck time, a parameter that is many orders of magnitude longer than the spin-lattice relaxation time. Any conclusion concerning quantum coherence is preliminary.

arXiv:cond-mat/0405501•May 21, 2004•0 citations
In this comment we show that the avian compass entanglement considerations of J. Cai, G. G. Guerreschi and H. J. Briegel (Phys. Rev. Lett. 104, 220502 (2010)) result in unphysical predictions on the magnetic sensitivity of this biochemical sensor. As well known from a series of papers on precision measurements and detailed derivations of standard quantum limits, not taking into account decoherence results in an overestimate of the entanglement lifetime, and this is the case at hand. The entanglement lifetime is wrongly assumed by the authors to be independent of the reaction time (the inverse of the recombination rate) and hence it is grossly overestimated. This is so because the spin coherence lifetime is limited by the reaction time, and the entanglement lifetime cannot be any longer.
The chemical compass model, based on radical pair reactions, is an idea to explain avian magnetoreception. At present, to the best of our knowledge, questions concerning the key ingredients responsible for the high sensitivity of a chemical compass and the possible role of quantum coherence and decoherence remain unsolved. Here, we investigate the optimized hyperfine coupling for a chemical compass in order to achieve the best magnetic field sensitivity. We show that its magnetic sensitivity limit can be further extended by simple quantum control and may benefit from additional decoherence. With this, we clearly demonstrate how quantum coherence can be exploited in the functioning of a chemical compass. The present results also provide routes toward the design of a biomimetic weak magnetic field sensor.
It is known that more than 50 species use the Earth's magnetic field for orientation and navigation. Intensive studies, particularly behavior experiments with birds, provide support for a chemical compass based on magnetically sensitive free radical reactions as a source of this sense. However, the fundamental question of how quantum coherence plays an essential role in such a chemical compass model of avian magnetoreception yet remains controversial. Here, we show that the essence of the chemical compass model can be understood in analogy to a quantum interferometer exploiting global quantum coherence rather than any subsystem coherence. Within the framework of quantum metrology, we quantify global quantum coherence and correlate it with the function of chemical magnetoreception. Our results allow us to understand and predict how various factors can affect the performance of a chemical compass from the unique perspective of quantum coherence assisted metrology. This represents a crucial step to affirm a direct connection between quantum coherence and the function of a chemical compass.
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 radical-pair mechanism is one of two distinct mechanisms used to explain the navigation of birds in geomagnetic fields, however little research has been done to explore the role of quantum entanglement in this mechanism. In this paper we study the lifetime of radical-pair entanglement corresponding to the magnitude and direction of magnetic fields to show that the entanglement lasts long enough in birds to be used for navigation. We also find that the birds appear to not be able to orient themselves directly based on radical-pair entanglement due to a lack of orientation sensitivity of the entanglement in the geomagnetic field. To explore the entanglement mechanism further, we propose a model in which the hyperfine interactions are replaced by local magnetic fields of similar strength. The entanglement of the radical pair in this model lasts longer and displays an angular sensitivity in weak magnetic fields, both of which are not present in previous models.
In a recent paper, cond-mat/0405331 (Ref. 1), del Barco et al. reported experimental studies on a Ni4 molecular system. They used an experimental method (combining microwave spectroscopy with high sensitivity magnetic measurements) that we have introduced before, cond-mat/0404410 (see also Ref. 2 and 3). Among other things, our technique allows us to monitor spin-state populations in the presence of microwave magnetic fields. Absorption line-widths give rough 'upper bounds' on the decoherence rate similar to 'standard' high frequency electron paramagnetic resonance (HF-EPR) techniques. In the case of quasi continuous radiation our technique does NOT give directly the spin-lattice relaxation time T1. For measurements like those of del Barco et al., it simply gives access to the phonon-bottleneck time, a parameter that is many orders of magnitude longer than the spin-lattice relaxation time. Any conclusion concerning quantum coherence is preliminary.