Local quantum uncertainty as a robust metric to characterize discord-like quantum correlations in subsets of the chromophores in photosynthetic light-harvesting complexes

M. Chávez-Huerta, F. Rojas


Green sulfur bacteria is a photosynthetic organism whose light-harvesting complex accommodates a pigment-protein complex called Fenna-Matthews-Olson (FMO). The FMO complex sustains quantum coherence and quantum correlations between the electronic states of spatially separated pigment molecules as energy moves with nearly a 100% quantum efficiency to the reaction center. We present a method based on the quantum uncertainty associated to local measurements to quantify discord-like quantum correlations between two subsystems where one is a qubit and the other is a qudit. We implement the method by calculating local quantum uncertainty (LQU), concurrence, and coherence between subsystems of pure and mixed states represented by the eigenstates and by the thermal equilibrium state determined by the FMO Hamiltonian. Three partitions of the seven chromophores network define the subsystems: one chromophore with six chromophores, pairs of chromophores, and one chromophore with two chromophores. Implementation of the LQU approach allows us to characterize quantum correlations that had not been studied before, identify the most quantum correlated subsets of chromophores, and determine that, in the strongest associations of chromophores, the LQU is a monotonically increasing function of the coherence.


Quantum Biology; Quantum Information; Quantum Correlations

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Mohseni, M., Omar, Y., Engel, G., Plenio, M.B., Quantum Effects in Biology (Cambridge University Press, New York, 2014)

Camara-Artigas, A., Blankenship, R. E., Allen, J. P., The structure of the FMO

protein from Chlorobium tepidum at 2.2 A resolution, Photosynthesis Research 75 (2003) 49–55.

Li, Y., Zhou, W., Blankenship, R. E., Allen, J. P., Crystal structure of the bacteri-

ochlorophyll a protein from Chlorobium tepidum, Journal of Molecular Biology 271 (1997) 456–471

Chin, A. W., Datta, A., Caruso, F., Huelga, S. F., Plenio, M. B., Noise-assisted energy transfer in quantum networks and light-harvesting complexes, New Journal of Physics 12 (2010) 065002

Streltsov, A., Adesso, G. Plenio, M. B., Colloquium: Quantum coherence as a resource, Rev. Mod. Phys. 89 (2017) 041003

Baumgratz, T., Cramer, M., Plenio, M. B., Quantifying Coherence, Physical Review Letters 113 (2014) 1–5

Winter, A., Yang, D., Operational Resource Theory of Coherence, Physical Review Letters 116 (2016) 120404

Engel, G. S., Calhoun, T. R., Read, E. L., Ahn, T. K., Mancal, T., Cheng, Y. C.,

Blankenship, R. E., Fleming, G. R., Evidence for wavelike energy transfer through

quantum coherence in photosynthetic systems, Nature 446 (2007) 782–786

Panitchayangkoon, G., Hayes, D., Fransted, K. A., Caram, J. R., Harel, E., Wen, J., Blankenship, R. E., Engel, G. S., Long-lived quantum coherence in photosynthetic complexes at physiological temperature, Proceedings of the National Academy of Sciences 107 (2010) 12766–12770

Panitchayangkoon, G., Voronine, D. V., Abramavicius, D., Caram, J. R., Lewis, N. H. C., Mukamel, S., Engel, G. S., Direct evidence of quantum transport in photosynthetic light-harvesting complexes, Proceedings of the National Academy of Sciences 108 (2011) 20908–20912

Rebentrost, P., Mohseni, M., Kassal1, I., Lloyd, S., Aspuru-Guzik, A., Environment-assisted quantum transport, New Journal of Physics 11 (2009) 033003

Mohseni, Ma., Rebentrost, P., Lloyd, S., Aspuru-Guzik, A., Environment-assisted quantum walks in photosynthetic energy transfer, The Journal of chemical physics 129 (2008) 174106

Olaya-Castro, A., Lee, C. F., Olsen, F. F., Johnson, N. F., Efficiency of energy transfer in a light-harvesting system under quantum coherence, Physical Review B 78 (2008) 085115

Caruso, F., Chin, A. W., Datta, A., Huelga, S. F., Plenio, M. B., Highly efficient energy excitation transfer in light-harvesting complexes: The fundamental role of noise-assisted transport, The Journal of Chemical Physics 131 (2009) 105106

Brixner, T., Stenger, J., Vaswani, H. M., Cho, M., Fleming, G. R., Exciton Analysis in 2D Electronic Spectroscopy, J.Phys. Chem. B. 109 (2005) 18230–18236

Brixner, T., Stenger, J., Vaswani, H. M., Cho, M., Blankenship, R. E., Fleming, G.R., Two-dimensional spectroscopy of electronic couplings in photosynthesis, Nature 434 (2005) 625–628

Ishizaki, A., Fleming, G.R., Theoretical examination of quantum coherence in a photosynthetic system at physiological temperature, PNAS vol.106 no. 41 (2009) 17255–17260

Nielsen, M. A., Chuang, I. L., Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2010)

Werlang, T., Souza, S., Fanchini, F.F., Villas Boas, C.J., Robustness of quantum discord to sudden death, Phys. Rev. A 80 (2009) 024103

Ferraro, A., Aolita, L., Cavalcanti, D.,Cucchietti, F.M., Acn, A., Almost all quantum states have nonclassical correlations, Phys. Rev. A 81 (2010) 052318

Datta, A., Shaji, A., Caves, C.M., Quantum discord and the power of one qubit, Phys. Rev. Lett. 100 (2008) 050502

Merali, Z., Quantum computing: The power of discord, Nature 474 (2011) 24-26

Park, J. J., Kim, K. H., Sagawa, T., Kim, S. W., Heat en-

gine driven by purely quantum information, Phys. Rev. Lett 111

(2013) 230402

Dakic, B., Lipp, Y. O., Ma, X., Ringbauer, M., Kropatschek, S., Barz, S., Paterek, T., Vedral, V., Zeilinger, A., Brukner, C., Walther, P., Quantum discord as resource for remote state preparation, Nature Physics 8 (2012) 666–670

Pirandola, S., Quantum discord as a resource for quantum cryptography Scientific Reports 4 : 6956 (2014) 1–5

Girolami, D., Souza, A. M., Giovannetti, V., Tufarelli, T., Filgueiras, J. G., Sarthour, R. S., Soares-Pinto, D. O., Oliveira, I. S., Adesso, G., Quantum Discord Determines the Interferometric Power of Quantum States, Phys. Rev. Lett. 112 (2014) 210401

Sarovar, M., Ishizaki, A., Fleming, G. R., Whaley, K. B., Quantum entanglement in photosynthetic light-harvesting complexes, Nature Physics 6 (2010) 462–467

Ishizaki, A., Fleming, G. R., Quantum superpositions in photosynthetic light harvesting: delocalization and entanglement, New Journal of Physics 12 (2010) 055004

Bradler, K., Wilde, M. M., Vinjanampathy, S., Uskov, D. B., Identifying the quantum correlations in light-harvesting complexes, Physical Review A 82 (2010) 062310

Sarovar, M., Ishizaki, A., Whaley, K. B., Quantum entanglement phenomena in photosynthetic light harvesting complexes, Procedia Chemistry 3 (2011) 152–164

Thilagam, A., Multipartite entanglement in the Fenna-Matthews-Olson (FMO) pigment-protein complex, Journal of Chemical Physics 136 (2012) 175104

Zhu, J., Kais, S., Aspuru-Guzik, A., Rodriques, S., Brock, B., Love, P. J., Multipartite quantum entanglement evolution in photosynthetic complexes, Journal of Chemical Physics 137 (2012) 074112

Chanda, T., Mishra, U., De, A. S., Sen, U., Time dynamics of multiparty quantum correlations indicate energy transfer route in light-harvesting complexes, arXiv:1412.6519 (2014)

Skochdopole, N., Mazziotti, D. A., Functional Subsystems and Quantum Redundancy in Photosynthetic Light Harvesting, Journal of Physical Chemistry Letters 2 (2011) 2989–2993

Caruso, F., Chin, A. W., Datta, A., Huelga, S. F., Plenio, M. B., Entanglement and entangling power of the dynamics in light-harvesting complexes, Physical Review A 81 (2010) 062346

Fassioli, F., Olaya-Castro, A: Distribution of entanglement in light-harvesting complexes and their quantum efficiency, New Journal of Physics 12 (2010) 085006

Scholak, T., De Melo, F., Wellens, T., Mintert, F., Buchleitner, A., Efficient and coherent excitation transfer across disordered molecular networks, Physical Review E. 83 (2011) 021912

Fernandes-Fanchini, F., Soares-Pinto, D. de O., Adesso, G., Lectures on General Quantum Correlations and their Applications (Springer International Publishing AG, Cham, 2017)

Girolami, D., Tufarelli, T., Adesso, G., Characterizing nonclassical correlations via local quantum uncertainty, Physical Review Letters 110 (2013) 1–5

Coulamy, I. B., Warnes, J. H., Sarandy, M. S., Saguia, A., Scaling of the local quantum uncertainty at quantum phase transitions, Physics Letters A. 380 (2016) 1724–1728

Sales, J. S., Cardoso, W. B., Avelar, A. T., De Almeida, N. G., Dynamics of nonclassical correlations via local quantum uncertainty for atom and field interacting into a lossy cavity QED, Physica A. 443 (2016) 399–405

Adolphs, J., Renger, T., How proteins trigger excitation energy transfer in the FMO complex of green sulfur bacteria, Biophysical Journal 91 (2006) 2778–2797

Hayes, D., Engel, G.S., Extracting the excitonic Hamiltonian of the Fenna-Matthews-Olson complex using three-dimensional third-order electronic spectroscopy, Biophysical Journal 100 (2011) 2043–2052

Audretsch, J., Entangled Systems: new directions in quantum physics. (WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim, 2007)

Modi, K., Brodutch, A., Cable, H., Paterek, T., Vedral, V., The classical-quantum boundary for correlations: Discord and related measures, Reviews of Modern Physics 84 (2012) 1655–1707

Luo, S., Wigner-Yanase Skew Information VS. Quantum Fisher Information, Proceedings of the American Mathematical Society 132 (2003) 885–890

Rafsanjani, S. M. H., Agarwal, S., X-matrices provide a lower bound of concurrence, arXiv: 1204.3912 (2012)

DOI: https://doi.org/10.31349/RevMexFis.66.525


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