In a recent Letter [Phys. Rev. Lett. 109, 110502 (2012), arXiv:1204.6528],
Bandyopadhyay, Paterek and Kaszlikowski report their analysis of spin coherence
time in the radical pair involved in avian magnetoreception, concluding that is
of the order of a microsecond. However, a combination of an erroneous numerical
calculation together with an incorrect parameter drawn from an experimental
source have resulted in the authors underestimating by two orders of magnitude.
Consequently, one must reverse the authors' conclusion that the timescale is
consistent with experiments on cryptochrome

Benjamin, Simon C.

Gauger, Erik M.

Physical Review Letters

English

arXiv

Gauger, EM

Benjamin, SC

Oxford University Research Archive (ORA)

Comment on "Quantum coherence and sensitivity of avian magnetoreception".

Heriot Watt Pure

    Heriot-Watt University Research Gateway                                                          Heriot-Watt UniversityComment on "Quantum Coherence and Sensitivity of Avian Magnetoreception"Gauger, Erik; Benjamin, Simon C.Published in:Physical Review LettersDOI:10.1103/PhysRevLett.110.178901Publication date:2013Link to publication in Heriot-Watt Research GatewayCitation for published version (APA):Gauger, E. M., & Benjamin, S. C. (2013). Comment on "Quantum Coherence and Sensitivity of AvianMagnetoreception". Physical Review Letters, 110(17), [178901]. 10.1103/PhysRevLett.110.178901General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Comment on ‘‘Quantum Coherence and Sensitivity ofAvian Magnetoreception’’Several papers [1–3] have studied the quantum physicsof the radical pair mechanism hypothesized to underlie theaviancompass. Our2011 Letter[2]analyzedthe coherencetime of the electron spin pair and found that it must besurprisingly long. To be consistent with behavioral studieson European Robins involving weak radio frequency (rf)ﬁelds [4,5], the coherence time should be of order 100  sor more. Interestingly, this is considerably longer than thereported 6  s radical pair lifetime from in vitro experi-ments on cryptochrome [6], widely considered a potentialcandidate for the avian compass [7].Utilizing the radical pair model we described in Ref. [2],Bandyopadhyay et al. seek to close this gap by consideringadditional behavioral studies, as reported in a very recentLetter [8]. However, their analysis suffers from two errors:an erroneous numerical computation together with theomissionofvitalexperimentaldata.Theseissuesaremulti-plicative and result in an underestimate of the lower boundby a factor of about 40. Consequently, the estimate of thelifetime given in the paper as 5–6:7  s, and described as‘‘of the order of a microsecond’’ in their abstract, in factbecomes 200–270  s, i.e., hundreds of microseconds.To test the validity of Bandyopadhyay-Paterek-Kaszlikowski’s (BPK) numerical calculation, we regener-ated their simulation results using exactly the model andtheparameterswhichtheyselect.Afteranexhaustiveseriesof simulations, we conclude that it is not possibleto reproduce the graphs in BPK’s Letter. One can matchthe line shapes exactly, but to do so one must rescale by afactor of four either the time axis or the spins’ g-factors.In an online document [9], we provide complete details ofour analysis for scrutiny. Furthermore, we have been madeaware that an independent researcher also found it impos-sible to reproduce BPK’s results without artiﬁcially scalingthemodelparameters[10].Evidently,thereisanerrorinthenumerical code employed by BPK.In deriving lifetime estimates, both our originalLetter and BKP’s vitally depend on the effect of weakresonant ﬁelds in disrupting the birds’ compass sense.Experimentalists have reported disruptions for ﬁelds ofstrength 470 nT to 15 nT. In our paper we took the valueof 150 nT to ensure a conservative estimate; however, toargue that a speciﬁc shorter process timescale is consistentwith the body of behavioral experiments, the analysisshould be based on the weakest rf ﬁeld known to disruptthe bird’s compass sense, i.e., 15 nT. BPK perform theircalculations for Brf ¼ 470, 150, and 47 nT, but inexplica-bly they omit the crucial 15 nT datum (see Fig. 3 ofRef. [5], which BPK cite as their Ref. [13]). The effect ofincluding this result is to increase the lower bound onthe lifetime by a factor of about 10, which becomes 40in view of the numerical error described above [9]. Statedalternatively: the timescale reported by BKP is not con-sistent with the reported disruption of the avian compassat ﬁelds of 15 nT; any bird whose compass lifetime isconﬁned to microseconds (or indeed 10s of microseconds)must be immune to a 15 nT oscillatory ﬁeld.BKP’s observation that long coherence is not requiredfor a compass sense remains correct. However, this is not anovel observation, having been stated and analyzed in our2011 Letter [2] and in Ref. [3]; the latter speciﬁcally exam-ined the cases where noise is beneﬁcial. Notwithstandingthe puzzle of why the bird should evolve an unnecessarilylong lifetime [11], the available data [4,5,12] applied to aproper quantum mechanical model of the radical pairmechanism nevertheless indeed imply that the life- andcoherence time is of order 100  s or more.Erik M. Gauger1,2,* and Simon C. Benjamin2,11Centre for Quantum TechnologiesNational University of Singapore3 Science Drive 2, 117543 Singapore2Department of MaterialsUniversity of OxfordParks Road, Oxford OX1 3PH, United KingdomReceived 7 December 2012; published 23 April 2013DOI: 10.1103/PhysRevLett.110.178901PACS numbers: 03.67. a, 03.65.Yz, 82.30. b*erik.gauger@materials.ox.ac.uk[1] J. Cai, G. Guerreschi, and H.J. Briegel, Phys. Rev. Lett.104, 220502 (2010).[2] E.M. Gauger, E. Rieper, J.J.L. Morton, S.C. Benjamin,and V. Vedral, Phys. Rev. Lett. 106, 40503 (2011).[3] J. Cai, F. Caruso, and M.B. Plenio, Phys. Rev. A 85,040304(R) (2012).[4] T. Ritz, P. Thalau, J.B. Phillips, R. Wiltschko, and W.Wiltschko, Nature (London) 429, 177 (2004).[5] T. Ritz, R. Wiltschko, P.J. Hore, C.T. Rodgers, K. Stapput,P. Thalau, C.R. Timmel, and W. Wiltschko, Biophys. J. 96,3451 (2009).[6] T. Biskup, E. Schleicher, A. Okafuji, G. Link, K. Hitomi,E.D. Getzoff, and S. Weber, Angew. Chem., Int. Ed. 48,404 (2009).[7] J.C.S. Lau, C.T. Rodgers, and P.J. Hore, J.R. Soc.J. R. Soc. Interface 9, 3329 (2012).[8] J. Bandyopadhyay, T. Paterek, and D. Kaszlikowski, Phys.Rev. Lett. 109, 110502 (2012).[9] Online Document, http://dx.doi.org/10.6084/m9.ﬁgshare.660856.[10] Neill Lambert (private communication).[11] A.M. Stoneham, E.M. Gauger, K. Porfyrakis, S.C.Benjamin, and B.W. Lovett, Biophys. J. 102, 961 (2012).[12] W. Wiltschko, K. Stapput, P. Thalau, and R. Wiltschko,Naturwissenschaften 93, 300 (2006).PRL 110, 178901 (2013) PHYSICAL REVIEW LETTERSweek ending26 APRIL 20130031-9007=13=110(17)=178901(1) 178901-1  2013 American Physical Society

Comment on "Quantum Coherence and Sensitivity of Avian Magnetoreception"

Comment on ‘‘Quantum Coherence and Sensitivity ofAvian Magnetoreception’’Several papers [1–3] have studied the quantum physicsof the radical pair mechanism hypothesized to underlie theavian compass. Our 2011 Letter [2] analyzed the coherencetime of the electron spin pair and found that it must besurprisingly long. To be consistent with behavioral studieson European Robins involving weak radio frequency (rf)fields [4,5], the coherence time should be of order 100 sor more. Interestingly, this is considerably longer than thereported 6 s radical pair lifetime from in vitro experi-ments on cryptochrome [6], widely considered a potentialcandidate for the avian compass [7].Utilizing the radical pair model we described in Ref. [2],Bandyopadhyay et al. seek to close this gap by consideringadditional behavioral studies, as reported in a very recentLetter [8]. However, their analysis suffers from two errors:an erroneous numerical computation together with theomission of vital experimental data. These issues are multi-plicative and result in an underestimate of the lower boundby a factor of about 40. Consequently, the estimate of thelifetime given in the paper as 5–6:7 s, and described as‘‘of the order of a microsecond’’ in their abstract, in factbecomes 200–270 s, i.e., hundreds of microseconds.To test the validity of Bandyopadhyay-Paterek-Kaszlikowski’s (BPK) numerical calculation, we regener-ated their simulation results using exactly the model andthe parameters which they select. After an exhaustive seriesof simulations, we conclude that it is not possibleto reproduce the graphs in BPK’s Letter. One can matchthe line shapes exactly, but to do so one must rescale by afactor of four either the time axis or the spins’ g-factors.In an online document [9], we provide complete details ofour analysis for scrutiny. Furthermore, we have been madeaware that an independent researcher also found it impos-sible to reproduce BPK’s results without artificially scalingthemodel parameters [10]. Evidently, there is an error in thenumerical code employed by BPK.In deriving lifetime estimates, both our originalLetter and BKP’s vitally depend on the effect of weakresonant fields in disrupting the birds’ compass sense.Experimentalists have reported disruptions for fields ofstrength 470 nT to 15 nT. In our paper we took the valueof 150 nT to ensure a conservative estimate; however, toargue that a specific shorter process timescale is consistentwith the body of behavioral experiments, the analysisshould be based on the weakest rf field known to disruptthe bird’s compass sense, i.e., 15 nT. BPK perform theircalculations for Brf ¼ 470, 150, and 47 nT, but inexplica-bly they omit the crucial 15 nT datum (see Fig. 3 ofRef. [5], which BPK cite as their Ref. [13]). The effect ofincluding this result is to increase the lower bound onthe lifetime by a factor of about 10, which becomes 40in view of the numerical error described above [9]. Statedalternatively: the timescale reported by BKP is not con-sistent with the reported disruption of the avian compassat fields of 15 nT; any bird whose compass lifetime isconfined to microseconds (or indeed 10s of microseconds)must be immune to a 15 nT oscillatory field.BKP’s observation that long coherence is not requiredfor a compass sense remains correct. However, this is not anovel observation, having been stated and analyzed in our2011 Letter [2] and in Ref. [3]; the latter specifically exam-ined the cases where noise is beneficial. Notwithstandingthe puzzle of why the bird should evolve an unnecessarilylong lifetime [11], the available data [4,5,12] applied to aproper quantum mechanical model of the radical pairmechanism nevertheless indeed imply that the life- andcoherence time is of order 100 s or more.Erik M. Gauger1,2,* and Simon C. Benjamin2,11Centre for Quantum TechnologiesNational University of Singapore3 Science Drive 2, 117543 Singapore2Department of MaterialsUniversity of OxfordParks Road, Oxford OX1 3PH, United KingdomReceived 7 December 2012; published 23 April 2013DOI: 10.1103/PhysRevLett.110.178901PACS numbers: 03.67.a, 03.65.Yz, 82.30.b*erik.gauger@materials.ox.ac.uk[1] J. Cai, G. Guerreschi, and H. J. Briegel, Phys. Rev. Lett.104, 220502 (2010).[2] E.M. Gauger, E. Rieper, J. J. L. Morton, S. C. Benjamin,and V. Vedral, Phys. Rev. Lett. 106, 40503 (2011).[3] J. Cai, F. Caruso, and M.B. Plenio, Phys. Rev. A 85,040304(R) (2012).[4] T. Ritz, P. Thalau, J. B. Phillips, R. Wiltschko, and W.Wiltschko, Nature (London) 429, 177 (2004).[5] T. Ritz, R. Wiltschko, P. J. Hore, C. T. Rodgers, K. Stapput,P. Thalau, C. R. Timmel, andW.Wiltschko, Biophys. J. 96,3451 (2009).[6] T. Biskup, E. Schleicher, A. Okafuji, G. Link, K. Hitomi,E. D. Getzoff, and S. Weber, Angew. Chem., Int. Ed. 48,404 (2009).[7] J. C. S. Lau, C. T. Rodgers, and P. J. Hore, J. R. Soc.J. R. Soc. Interface 9, 3329 (2012).[8] J. Bandyopadhyay, T. Paterek, and D. Kaszlikowski, Phys.Rev. Lett. 109, 110502 (2012).[9] Online Document, http://dx.doi.org/10.6084/m9.figshare.660856.[10] Neill Lambert (private communication).[11] A.M. Stoneham, E.M. Gauger, K. Porfyrakis, S. C.Benjamin, and B.W. Lovett, Biophys. J. 102, 961 (2012).[12] W. Wiltschko, K. Stapput, P. Thalau, and R. Wiltschko,Naturwissenschaften 93, 300 (2006).PRL 110, 178901 (2013) P HY S I CA L R EV I EW LE T T E R Sweek ending26 APRIL 20130031-9007=13=110(17)=178901(1) 178901-1  2013 American Physical Society

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