![(a) Entanglement measure of the excitonic qubit subsystem, Ea as function of time t (ps) and γ0 (cm −1 ), evaluated for the W state (Eq.(17) using Eqs.(5) and (7). The detuning parameter, δ =0. ∆ω=80 cm −1 [87] in Eq.(9). The parameter estimates are typical of the FMO complex of P. aestuarii [87] (b) Same as in (a) except that the entanglement measure of the system of the collective reservoir states Er is obtained as a function of t (ps) and γ0 (cm −1 )](https://www.researchgate.net/profile/Alagu-Thilagam/publication/224956134/figure/fig9/AS:667090063196171@1536058073786/a-Entanglement-measure-of-the-excitonic-qubit-subsystem-Ea-as-function-of-time-t-ps_Q320.jpg)
![(a) Teleportation fidelity, F GHZ , as a function of time t (ps) and γ0 [10 cm −1 (blue line), 50 cm −1 (green line), 1000 cm −1 (red line)] based on the GHZ resource states, using Eq. (25). The detuning parameter is set at δ =0 and N =4. ∆ω=80 cm −1 [87] in Eq.(9). The classical fidelity of 2/3 is denoted by dotted lines. (b) Same as in (a) except N =16 (c) Same as in (a) except N =64](https://www.researchgate.net/profile/Alagu-Thilagam/publication/224956134/figure/fig11/AS:667090063200283@1536058073903/a-Teleportation-fidelity-F-GHZ-as-a-function-of-time-t-ps-and-g0-10-cm-1-blue_Q320.jpg)
![(a) Quantum information splitting fidelity, F GHZS , as a function of time t (ps) and γ0 [10 cm −1 (blue line), 50 cm −1 (green line), 1000 cm −1 (red line)] based on the GHZ resource states, using Eq. (27). The detuning parameter is set at δ =0 and N =4. ∆ω=80 cm −1 [87] in Eq.(9). The classical fidelity of 2/3 is denoted by dotted lines. (b) Same as in (a), except N =16 (c) Same as in (a) except N =64](https://www.researchgate.net/profile/Alagu-Thilagam/publication/224956134/figure/fig12/AS:667090063216652@1536058073978/a-Quantum-information-splitting-fidelity-F-GHZS-as-a-function-of-time-t-ps-and-g0_Q320.jpg)
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Multipartite entanglement in the Fenna-Matthews-Olson (FMO) pigment-protein complex
Abstract and Figures
We investigate multipartite states in the Fenna-Matthews-Olson (FMO) pigment-protein complex of the green sulfur bacteria using a Lorentzian spectral density of the phonon reservoir fitted with typical parameter estimates of the species, Prosthecochloris aestuarii. The evolution of the entanglement measure of the excitonic W qubit states is evaluated in the picosecond time range, showing increased revivals in the non-Markovian regime. Similar trends are observed in the evolution dynamics of the Meyer-Wallach measure of the N-exciton multipartite state, with results showing that multipartite entanglement can last from 0.5 to 1 ps, between the bacteriochlorophylls of the FMO complex. The teleportation and quantum information splitting fidelities associated with the Greenberger-Horne-Zeilinger and W-like resource states formed by the excitonic qubit channels of the FMO complex show that revivals in fidelities increase with the degree of non-Markovian strength of the decoherent environment. Quantum information processing tasks involving teleportation followed by the decodification process involving W-like states of the FMO complex may play a critical role during coherent oscillations at physiological temperatures.
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... Nevertheless, this measure has inherent deficiencies, as it is unable to distinguish fully non-separable states from those with separable subsystems. Despite this, it is useful for obtaining a global vision of entanglement in the group of N BChls [70]. ...
... An alternative approach to provide a global measure of entanglement is a weighted average of entanglement entropies upon all bipartitioned groups of BCHls [70,71]: [63] has commonly been used [70]: ...
... An alternative approach to provide a global measure of entanglement is a weighted average of entanglement entropies upon all bipartitioned groups of BCHls [70,71]: [63] has commonly been used [70]: ...
Fenna-Mathews-Olson complexes participate in the photosynthetic process of Sulfur Green Bacteria. These biological subsystems exhibit quantum features which possibly are responsible for their high efficiency; the latter may comprise multipartite entanglement and the apparent tunnelling of the initial quantum state. At first, to study these aspects, a multidisciplinary approach including experimental biology, spectroscopy, physics, and math modelling is required. Then, a global computer modelling analysis is achieved in the computational biology domain. The current work implements the Hierarchical Equations of Motion to numerically solve the open quantum system problem regarding this complex. The time-evolved states obtained with this method are then analysed under several measures of entanglement, some of them already proposed in the literature. However, for the first time, the maximum overlap with respect to the closest separable state is employed. This authentic multipartite entanglement measure provides information on the correlations, not only based on the system bipartitions as in the usual analysis. Our study has led us to note a different view of FMO multipartite entanglement as tiny contributions to the global entanglement suggested by other more basic measurements. Additionally, in another related trend, the initial state, considered as a Förster Resonance Energy Transfer, is tracked using a novel approach, considering how it could be followed under the fidelity measure on all possible permutations of the FMO subsystems through its dynamical evolution by observing the tunnelling in the most probable locations. Both analyses demanded significant computational work, making for a clear example of the complexity required in computational biology.
... This co-enzyme forms the basis for critical cellular processes needed for survival of the supported species. The theory of excitonic energy transfer in light harvesting systems (LHS) has been a topic of interest over several decades [1][2][3][4][5][8][9][10][11][12][13][14][15][16][17][18][19][20]. The light harvesting complexes from different species vary in their structural arrangements, but possess the common attribute of enabling excitation propagation even in adverse, noisy environments. ...
... where ξ = (∆ω/2 − iδ) 2 − γ 0 ∆ω. The exciton population difference, ∆P , a signature of coherence, has been evaluated [12] using |u(t)| 2 (Eq. (8). ...
... (8). The results in Ref. [12] show that at small ∆ω/2 ∼20 cm −1 or large reservoir correlation times and large γ 0 (or small exciton relaxation times), there is increased time period (up to 1 ps) over which the population difference, ∆P remains resilient. This appears to be in agreement experimental results of the FMO complex of P. aestuarii [98]. ...
In natural light harvesting systems, the sequential quantum events of photon
absorption by specialized biological antenna complexes, charge separation,
exciton formation and energy transfer to localized reaction centers culminates
in the conversion of solar to chemical energy. A notable feature in these
processes is the exceptionally high efficiencies (> 95 %) at which excitation
is transferred from the illuminated protein complex site to the reaction
centers. Such high exciton propagation rates within a system of interwoven
biomolecular network structures, is yet to be replicated in artificial light
harvesting complexes. A clue to unraveling the quantum puzzles of nature may
lie in the observation of long lived coherences lasting several picoseconds in
the electronic spectra of photosynthetic complexes, even in noisy environmental
baths. A number of experimental and theoretical studies have been devoted to
unlocking the links between quantum processes and information protocols, in the
hope of finding answers to nature's puzzling mode of energy propagation. This
review presents developments in quantum theories, and links
information-theoretic aspects with photosynthetic light-harvesting processes in
biomolecular systems. There is examination of various attempts to pinpoint the
processes that underpin coherence features arising from the light harvesting
activities of biomolecular systems, with particular emphasis on the effects
that factors such non-Markovianity, zeno mechanisms, teleportation, quantum
predictability and the role of multipartite states have on the quantum dynamics
of biomolecular systems. A discussion of how quantum thermodynamical principles
and agent-based modeling and simulation approaches can improve our
understanding of natural photosynthetic systems is included.
... The corresponding success probabilities, denoted as P opt III (p,t) and P opt IV (p,t) with respect to the two types of second measurements, can be constructed in the same way from (13) and (14) as (16) and ...
... To specify the structure of the bath, we consider a Lorentzian spectral density of the form [15][16][17] ...
On-demand measurement-based schemes to control coherence transfer between interacting qubits inside
a dissipative environment are considered. The measurements employed are of the types of quantum weak
measurement and quantum reversal measurement of which one is carried out at the beginning of the system evolution t = 0 and the other at a later intended timet > 0. The relevant questions are which type of measurement should be performed at t = 0 and which type at t > 0, as well as which strength of the second measurement should be chosen in dependence on the strength of the first measurement to optimally achieve a demand? We answer such questions in this work as to meet two concrete demands, namely, to make optimal (i) the transfer of coherence from the sth qubit to the rth qubit and (ii) the preservation of coherence at the sth qubit. Particularly, independent of the coherence degree of the sth qubit at t = 0, the coherence degree of either the rth qubit or the sth qubit at any t > 0 can be made arbitrarily close to the maximum value equal to 1/2, but at the cost of vanishingly reduced success probability. As an application, we discuss the coherence transfer between two qubits of a bipartite system.We also analyze the influence of the controlling schemes for optimal coherence transfer on the degree of entanglement created at t > 0 between the two qubits.
... Various theories [27,[29][30][31][32][33] have been proposed in recent years to account for the high efficiencies of energy transfer in the FMO protein complex. Ishizaki et. ...
... al. [29] showed that quantum coherence allows excitations to propagate without being trapped at sites with lower energies, while the role of a critical ratio in quantum coherence and environmental noise in achieving optimal functionality and efficiency in photosynthetic systems was examined in other works [27,33]. In an earlier work, we showed that quantum information processing tasks involving teleportation and decodification based on specific states (W -like states) of the FMO complex may contribute to coherent oscillations at physiological temperatures [32]. Recently, we considered the importance of the Zeno mechanism-non-Markovianity link [34] in wider networked molecular systems of photosynthetic membrane surfaces that constitute thousands of bacteriochorophylls. ...
We examine the coherent propagation of the one-dimensional Frenkel exciton
(correlated electron-hole pair system) based on a model of a quantum walker in
multi-dimensional Hilbert space. The walk is governed by a non-Hermitian coin
flip operation that is coupled to a generalized shift mechanism. The
dissipative coin flip operation is associated with amplitude leakages at an
occupied site, typical of processes which occur when an exciton is transferred
along dimer sites in photosynthetic protein complexes. We analyze the
characteristics probability distribution of the one-dimensional quantum walk
for various system parameters, and examine the complex interplay between
non-Markovian signatures and amplitude leakages within the Hilbert position
subspace. Can topological defects such as exceptional points, and non-Markovian
signatures be detected from a time evolving reconstructed excitonic state
density matrix using quantum tomography measurements? We examine these
possibilities in the broader context of a quantum information theoretic
approach to spectroscopic experiments.
... Investigations in the energy transfer dynamics of the FMO complex have revealed the existence of bipartite and global entanglement between the electronic states of spatially separated chromophores [14,[27][28][29][30][31]. These studies of excitation dynamics in the FMO protein show that entanglement lasts for 1-2 ps under Markovian models and for over 4 ps under more accurate non-Markovian models. ...
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.
... The focus of this work is an analysis of entanglement on a fundamental level. However, it should be pointed out that entanglement of electronic excitations has also been discussed in more applied works, e.g., in the context of photosynthesis 48,49 and quantum computing. 47,50 II. ...
A new perspective into correlation effects in electronically excited states is provided through quantum information theory. The entanglement between the electron and hole quasiparticles is examined, and it is shown that the related entanglement
entropy can be computed from the eigenvalue spectrum of the well-known natural transition orbital (NTO) decomposition. Non-vanishing entanglement is obtained whenever more than one NTO pair is involved, i.e., in the case of a multiconfigurational or collective excitation. An important implication is that in the case of entanglement it is not possible to gain a complete description of the state character from the orbitals alone, but more specific analysis methods are required to decode the mutual information between the electron and hole. Moreover, the newly introduced number of entangled states is an important property by itself giving information about excitonic structure. The utility of the formalism is illustrated in the cases of the excited states of two interacting ethylene molecules, the conjugated polymer para-phenylene vinylene, and the naphthalene molecule.
... The FMO complex trimer is made up of three symmetry equivalent monomer subunits, with each unit constituting eight bacteriochlorophyll (BChl)a molecules supported by a cage of protein molecules. The FMO complex acts as an efficient channel of excitation transfer in which photons captured in the chlorosome which is the main light harvesting antenna complex, are directed via a series of excitonic exchanges to a reaction center (RC) where energy conversion into a chemical form occurs. Long-lived coherences between electronic states lasting several picoseconds, much shorter than the 1 ns dissipative lifetimes of excitons [35], have been a topic of intense investigation in recent years [36][37][38]53]. Currently it is still not clear as to how biological systems comprising hundreds of photosynthetic complexes and many more correlated excitonic states act in unison to maintain the quantum coherences in the noisy environment, and attain the much envied high efficiencies at psychological temperatures. ...
We study the quantum dynamics of conversion of composite bosons into fermionic fragment species with increasing densities of bound fermion pairs using the open quantum system approach. The Hilbert space of N-state-functions is decomposed into a composite boson subspace and an orthogonal fragment subspace of quasi-free fermions that enlarges as the composite boson constituents deviate from ideal boson commutation relations. The tunneling dynamics of coupled composite bosons states in confined systems is examined, and the appearance of exceptional points under experimentally testable conditions (densities, lattice temperatures) is highlighted. The theory is extended to examine the energy transfer between macroscopically coherent systems such as multichromophoric macromolecules in photosynthetic light harvesting complexes.
We examine a simple scheme to generate genuine multipartite entangled states across disjoint qubit registers. We employ a shuttle qubit that is sequentially coupled, in an energy preserving manner, to the constituents within each register through rounds of interactions. We establish that stable W-type entanglement can be generated among all qubits within the registers. Furthermore, we find that the entanglement is sensitive to how the shuttle is treated, showing that a significantly larger degree is achieved by performing projective measurements on it. Finally, we assess the resilience of this entanglement generation protocol to several types of noise and imperfections, showing that it is remarkably robust.
The factors which govern the subtle links between follicle loss and mammalian female reproductive ageing remain unclear despite extensive studies undertaken to understand the critical physiological and biochemical mechanisms that underly the accelerated decline in follicle numbers in women older than 37 years. It is not certain whether there is a sole control by the ovary or whether other factors which affect ageing also intersect with the ovarian effect. There is convincing experimental evidence for an interplay of several processes that seem to influence the follicle loss-female reproductive ageing links, with specific hormones (follicle-stimulating hormone, anti-Müllerian hormone, dehydroepiandrosterone) noted to play important roles in follicular dynamics and ovarian ageing. In this work, we examine the subtle links between the rate of follicular decline with ageing and the role of hormones via a series of non-autonomous equations. Simulation results based on the time evolution of the number of ovarian follicles and biochemical changes in the ovarian environment influenced by hormone levels is compared with empirical data based on follicle loss-reproductive ageing correlation studies.
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The effect of measurement attributes (quantum level of precision, finite duration) on the classical and quantum correlations is analyzed for a pair of qubits immersed in a common reservoir. We show that the quantum discord is enhanced as the precision of the measuring instrument is increased, and both the classical correlation and the quantum discord experience noticeable changes during finite-time measurements performed on a neighboring partition of the entangled system. The implication of these results on the "information---disturbance relationship" is examined, with critical analysis of the delicate roles played by quantum non-locality and non-Markovian dynamics in the violation of this relationship, which appears surprisingly for a range of measurement attributes. This work highlights that the fundamental limits of quantum mechanical measurements can be altered by exchanges of non-classical correlations such as the quantum discord with external sources, which has relevance to cryptographic technology.
Anoxygenic Photosynthetic Bacteria is a comprehensive volume describing all aspects of non-oxygen-evolving photosynthetic bacteria. The 62 chapters are organized into themes of: Taxonomy, physiology and ecology; Molecular structure of pigments and cofactors; Membrane and cell wall structure: Antenna structure and function; Reaction center structure and electron/proton pathways; Cyclic electron transfer; Metabolic processes; Genetics; Regulation of gene expression, and applications. The chapters have all been written by leading experts and present in detail the current understanding of these versatile microorganisms.
The book is intended for use by advanced undergraduate and graduate students and senior researchers in the areas of microbiology, genetics, biochemistry, biophysics and biotechnology.
Editorial. Preface. Color Plates. I: Introduction to Light-Harvesting. 1. Photosynthetic Membranes and Their Light-Harvesting Antennas B.R. Green, J.M. Anderson, W.W. Parson. 2. The Pigments H. Scheer. 3. Optical Spectroscopy in Photosynthetic Antennas W.W. Parson, V. Nagarajan. 4. The Evolution of Light-Harvesting Antennas B.R. Green. II: Structure and Function in Light-Harvesting. 5. The Light-Harvesting System of Purple Bacteria B. Robert, R.J. Cogdell, R. van Grondelle. 6. Antenna Complexes from Green Photosynthetic Bacteria R.E. Blankenship, K. Matsuura. 7. Light-Harvesting in Photosystem II H. van Amerongen, J.P. Dekker. 8. Structure and Function of the Antenna System in Photsystem I P. Fromme, E. Schlodder, S. Jansson. 9. Antenna Systems and Energy Transfer in Cyanophyta and Rhodophyta M. Mimuro, H. Kikuchi. 10. Antenna Systems of Red Algae: Phycobilisomes with Photosystem II and Chlorophyll Complexes with Photosystem I E. Gantt, B. Grabowski, F.X. Cunningham Jr. 11. Light-Harvesting Systems in Chlorophyll c-Containing Algae A.N. Macpherson, R.G. Hiller. III: Biogenesis, Regulation and Adaptation. 12. Biogenesis of Green Plant Thylakoid Membranes K. Cline. 13. Pulse Amplitude Modulated Chlorophyll Fluorometry and its Application in Plant Science G.H. Krause, P. Jahns. 14. Photostasis in Plants, Green Algae and Cyanobacteria: The Role of Light-Harvesting Antenna Complexes N.P.A. Huner, G. Oquist, A. Melis. 15. Photoacclimation of Light-Harvesting Systems in EukaryoticAlgae P.G. Falkowski, Yi-Bu Chen. 16. Multi-level Regulation of Purple Bacterial Light-Harvesting Complexes C.S. Young, J.T. Beatty. 17. Environmental Regulation of Phycobilisome Biosynthesis A.R. Grossman, L.G. van Waasbergen, D. Kehoe. Index.
The notion of quantum discord introduced by Ollivier and Zurek [Phys. Rev. Lett 88 (2001) 017901] (see also Henderson and Vedral [J. Phys. A 34 (2001) 6899] ) has attracted increasing attention, in recent years, as an entropic quantifier of non-classical features pertaining to the correlations exhibited by bipartite quantum systems. Here we generalize the notion so as to encompass power-law qq-entropies (that reduce to the standard Shannon entropy in the limit q→1q→1) and study the concomitant consequences. The ensuing, new discord-like measures we advance describe aspects of non-classicality that are different from those associated with the standard quantum discord. A particular manifestation of this difference concerns a feature related to order. Let D1D1 stand for the standard, Shannon-based discord measure and DqDq for the q≠1q≠1 one. If two quantum states A,BA,B are such that D1(A)>D1(B)D1(A)>D1(B), this order-relation does not remain invariant under a change from D1D1 to DqDq.
Light, or electromagnetic wave, is the most powerful tool for probing the quantum mechanical motions of electrons and nuclei within molecules and condensed matter. Optical Processes in Solids describes the principles of this spectroscopic study with the help of illustrative comparisons of theoretical and experimental results that take into account the revolutionary progress brought about by the use of intense lasers and high-energy synchrotron light. In the final chapter Yutaka Toyozawa presents a speculative scenario on how solar light may have caused chemical reactions among atoms and molecules, leading to the creation and evolution of life on earth.
We revisit the relationship between entanglement and purity of states of two-qubits systems, using the q-entropies as measures of the degree of mixture. The q-entropies depend on the density matrix eigenvalues p(i) through the quantity omega(q) = Sigma(i)p(i)(q). Renyi's measures constitutes particular instances of these entropies. We pay particular attention to the case q = 2 and to the limit case q --> infinity. We provide analytical support to numerical results recently reported in the literature.
It is demonstrated that the premisses of the Einstein-Podolsky-Rosen
paper are inconsistent when applied to quantum systems consisting of at
least three particles. The demonstration reveals that the EPR program
contradicts quantum mechanics even for the cases of perfect
correlations. By perfect correlations is meant arrangements by which the
result of the measurement on one particle can be predicted with
certainty given the outcomes of measurements on the other particles of
the system. This incompatibility with quantum mechanics is stronger than
the one previously revealed for two-particle systems by Bell's
inequality, where no contradiction arises at the level of perfect
correlations. Both spin-correlation and multiparticle interferometry
examples are given of suitable three- and four-particle arrangements,
both at the gedanken and at the real experiment level.
By considering a radiating gas as a single quantum-mechanical system, energy levels corresponding to certain correlations between individual molecules are described. Spontaneous emission of radiation in a transition between two such levels leads to the emission of coherent radiation. The discussion is limited first to a gas of dimension small compared with a wavelength. Spontaneous radiation rates and natural line breadths are calculated. For a gas of large extent the effect of photon recoil momentum on coherence is calculated. The effect of a radiation pulse in exciting "super-radiant" states is discussed. The angular correlation between successive photons spontaneously emitted by a gas initially in thermal equilibrium is calculated.
The three-dimensional structure of a chlorophyll-containing protein has
been determined by X-ray crystallography and shown to consist of three
identical subunits, each containing a core of seven bacteriochlorophylls
arranged in an irregular fashion and enclosed within an envelope of
protein.