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arXiv:1202.4519 · The Journal of Chemical Physics

Multipartite quantum entanglement evolution in photosynthetic complexes

Jing Zhu, Sabre Kais, Alán Aspuru‐Guzik, Sam Rodriques, Benjamin L. Brock, Peter J. Love

Published Aug 21, 2012• 49 citations
arXivHTMLPDF

Abstract

We investigate the evolution of entanglement in the Fenna-Matthew-Olson (FMO) complex based on simulations using the scaled hierarchical equations of motion approach. We examine the role of entanglement in the FMO complex by direct computation of the convex roof. We use monogamy to give a lower bound for entanglement and obtain an upper bound from the evaluation of the convex roof. Examination of bipartite measures for all possible bipartitions provides a complete picture of the multipartite entanglement. Our results support the hypothesis that entanglement is maximum primary along the two distinct electronic energy transfer pathways. In addition, we note that the structure of multipartite entanglement is quite simple, suggesting that there are constraints on the mixed state entanglement beyond those due to monogamy.

DOI
10.1063/1.4742333

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Titas Chanda, Utkarsh Mishra, Aditi Sen De +1 more

The time-evolution of multiparty quantum correlations as quantified by monogamy scores and bipartition collections of quantum correlations is investigated for light-harvesting complexes modeled by the fully connected and the Fenna-Mathews-Olson (FMO) networks. The dynamics consists of a coherent term as well as dissipative, dephasing, and sink operator terms. The multiparty quantum correlation reveals important information regarding the sharability of quantum correlations in the networks, which allow us to categorize the network sites into three distinct groups in the FMO complex and to predict the structural geometry of the complex. In particular, we show that the relative values of the ingredients of multiparty quantum correlation measures in the time dynamics clearly indicate the primary route of energy transfer from the antenna to the bacterial reaction center in the FMO complex.

arXiv:1412.6519•Dec 19, 2014•6 citations
We investigate the evolution of entanglement in the Fenna-Matthew-Olson (FMO) complex based on simulations using the scaled hierarchical equations of motion approach. We examine the role of entanglement in the FMO complex by direct computation of the convex roof. We use monogamy to give a lower bound for entanglement and obtain an upper bound from the evaluation of the convex roof. Examination of bipartite measures for all possible bipartitions provides a complete picture of the multipartite entanglement. Our results support the hypothesis that entanglement is maximum primary along the two distinct electronic energy transfer pathways. In addition, we note that the structure of multipartite entanglement is quite simple, suggesting that there are constraints on the mixed state entanglement beyond those due to monogamy.
Applications of the concepts of quantum information theory are usually related to the powerful and counter-intuitive quantum mechanical effects of superposition, interference and entanglement. In this thesis, I examine the role of coherence and entanglement in complex chemical systems. The research has focused mainly on two related projects: The first project is developing a theoretical model to explain the recent ultrafast experiments on excitonic migration in photosynthetic complexes that show long-lived coherence of the order of hundreds of femtoseconds and the second project developing the Grover algorithm for global optimization of complex systems. The first part can be divided into two sections. The first section is investigating the theoretical frame about the transfer of electronic excitation energy through the Fenna-Matthews-Olson (FMO) pigment-protein complex. The new developed modified scaled hierarchical equation of motion (HEOM) approach is employed for simulating the open quantum system. The second section is investigating the evolution of entanglement in the FMO complex based on the simulation result via scaled HEOM approach. We examine the role of multipartite entanglement in the FMO complex by direct computation of the convex roof optimization for a number of different measures, including pairwise, triplet, quadruple and quintuple sites entanglement. Our results support the hypothesis that multipartite entanglement is maximum primary along the two distinct electronic energy transfer pathways. The second part of this thesis can be separated into two sections. The first section demonstrated that a modified Grover's quantum algorithm can be applied to real problems of finding a global minimum using modest numbers of quantum bits. Calculations of the global minimum of simple test functions and Lennard-Jones clusters have been carried out on a quantum computer simulator using a modified Grover's algorithm. The second section is implementing the basic quantum logical gates upon arrays of trapped ultracold polar molecules as qubits for the quantum computer. Utilized herein is the Multi-Target Optimal Control Theory (MTOCT) as a means of manipulating the initial-to-target transition probability via external laser field. The detailed calculation is applied for the SrO molecule, an ideal candidate in proposed quantum computers using arrays of trapped ultra-cold polar molecules.
The Fenna-Matthews-Olson (FMO) complex - a pigment protein complex involved in photosynthesis in green sulfur bacteria - is remarkably efficient in transferring excitation energy from light harvesting antenna molecules to a reaction center. Recent experimental and theoretical studies suggest that quantum coherence and entanglement may play a role in this excitation energy transfer (EET). We examine whether bipartite quantum nonlocality, a property that expresses a stronger-than-entanglement form of correlation, exists between different pairs of chromophores in the FMO complex when modeling the EET by the hierarchically coupled equations of motion method. We compare the results for nonlocality with the amount of bipartite entanglement in the system. In particular, we analyze in what way these correlation properties are affected by different initial conditions. It is found that bipartite nonlocality only exists when the initial conditions are chosen in an unphysiological manner and probably is absent when considering the EET in the FMO complex in its natural habitat. It is also seen that nonlocality and entanglement behave quite differently in this system. In particular, for localized initial states, nonlocality only exists on a very short time scale and then drops to zero in an abrupt manner. As already known from previous studies, quantum entanglement between chromophore pairs on the other hand is oscillating and exponentially decaying and follow thereby a pattern more similar to the chromophore population dynamics. The abrupt disappearance of nonlocality in the presence of nonvanishing entanglement is a phenomenon we call nonlocality sudden death; a striking manifestation of the difference between these two types of correlations in quantum systems.
The Fenna-Matthews-Olson (FMO) complex - a pigment protein complex involved in photosynthesis in green sulfur bacteria - is remarkably efficient in transferring excitation energy from light harvesting antenna molecules to a reaction center. Recent experimental and theoretical studies suggest that quantum coherence and entanglement may play a role in this excitation energy transfer (EET). We examine whether bipartite quantum nonlocality, a property that expresses a stronger-than-entanglement form of correlation, exists between different pairs of chromophores in the FMO complex when modeling the EET by the hierarchically coupled equations of motion method. We compare the results for nonlocality with the amount of bipartite entanglement in the system. In particular, we analyze in what way these correlation properties are affected by different initial conditions. It is found that bipartite nonlocality only exists when the initial conditions are chosen in an unphysiological manner and probably is absent when considering the EET in the FMO complex in its natural habitat. It is also seen that nonlocality and entanglement behave quite differently in this system. In particular, for localized initial states, nonlocality only exists on a very short time scale and then drops to zero in an abrupt manner. As already known from previous studies, quantum entanglement between chromophore pairs on the other hand is oscillating and exponentially decaying and follow thereby a pattern more similar to the chromophore population dynamics. The abrupt disappearance of nonlocality in the presence of nonvanishing entanglement is a phenomenon we call nonlocality sudden death; a striking manifestation of the difference between these two types of correlations in quantum systems.
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.
Abstract The Fenna-Matthews-Olson light-harvesting complexes have become a center of attention due to their high excitation energy transfer efficiency, which may surpass 98%. Experimental results reveal the presence of quantum entanglement in the protein structure, which seems to be associated to such a remarkably high efficiency. Notably, Redfield and Lindblad master equations have been already used to model the chromophore excitation in the protein complex as well as its interactions with the environment. The entanglement arising during the process has been quantified through several measures. This work provides a short review of methods used to model the above described system. It is also discussed the introduction of two nonconventional measures addresed to quantify the emergent entanglement.
The time-evolution of multiparty quantum correlations as quantified by monogamy scores and bipartition collections of quantum correlations is investigated for light-harvesting complexes modeled by the fully connected and the Fenna-Mathews-Olson (FMO) networks. The dynamics consists of a coherent term as well as dissipative, dephasing, and sink operator terms. The multiparty quantum correlation reveals important information regarding the sharability of quantum correlations in the networks, which allow us to categorize the network sites into three distinct groups in the FMO complex and to predict the structural geometry of the complex. In particular, we show that the relative values of the ingredients of multiparty quantum correlation measures in the time dynamics clearly indicate the primary route of energy transfer from the antenna to the bacterial reaction center in the FMO complex.