Quantum coherence in biological systems is often assumed to be thermodynamically expensive to maintain, but its actual energy cost has never been quantified. We compute the thermodynamic cost of quantum-coherent energy transfer in the FMO photosynthetic complex using Lindblad master equation simulations. At optimal ENAQT dephasing (γ = 100 cm⁻¹), the transport efficiency reaches 29.4%, the Holevo channel capacity peaks at 2.17 bits, and the Landauer ratio—the energy cost per successfully transmitted bit relative to the fundamental thermodynamic limit kT ln 2—is ~ 390×. This is approximately 104 times more efficient than classical CMOS computing (~ 107× Landauer). The entropy production rate peaks at 1.77 kB/ps at γ = 300 cm⁻¹, and the von Neumann entropy saturates at Smax = 2.45 bits at steady state. These results provide the first quantitative thermodynamic characterization of quantum-coherent energy transfer in a pigment-protein complex.
Quantum coherence in biological systems is often assumed to be thermodynamically expensive to maintain, but its actual energy cost has never been quantified. We compute the thermodynamic cost of quantum-coherent energy transfer in the FMO photosynthetic complex using Lindblad master equation simulations. At optimal ENAQT dephasing (γ = 100 cm⁻¹), the transport efficiency reaches 29.4%, the Holevo channel capacity peaks at 2.17 bits, and the Landauer ratio—the energy cost per successfully transmitted bit relative to the fundamental thermodynamic limit kT ln 2—is ~ 390×. This is approximately 104 times more efficient than classical CMOS computing (~ 107× Landauer). The entropy production rate peaks at 1.77 kB/ps at γ = 300 cm⁻¹, and the von Neumann entropy saturates at Smax = 2.45 bits at steady state. These results provide the first quantitative thermodynamic characterization of quantum-coherent energy transfer in a pigment-protein complex.
In this work, energy transfer in the photosynthetic process was studied from a quantum perspective, using the Fenna–Matthews–Olson (FMO) complex as a model. The density operator formalism and the Lindblad master equation were employed to describe the non-unitary dynamics of an open system subject to injection, extraction, and decoherence processes. A two-level system and a three-site FMO complex were analyzed, allowing the study of phenomena such as Rabi oscillations, environment-induced coherence loss, and the emergence of Environment-Assisted Quantum Transport (ENAQT). Through numerical simulations, exciton and heat currents, von Neumann entropy, global and intersite entanglement, and energy transfer efficiency were calculated. The results show that, far from being an obstacle, the interaction with the environment can enhance photosynthetic efficiency under intermediate noise regimes, thus validating the ENAQT hypothesis. This study confirms that photosynthetic systems exploit a delicate balance between coherence and decoherence to optimize energy transport.
Quantum Darwinism—the redundant proliferation of quantum information into the environment—is the leading framework for understanding how classical reality emerges from quantum mechanics but has never been experimentally demonstrated in a biological system. We apply the Quantum Darwinism framework to the FMO photosynthetic complex, treating the input chromophore site 1 as the "system" and the remaining six sites as the "environment." Using Lindblad master equation simulations at physiological dephasing (γ = 175 cm⁻¹), we compute partial information curves, redundancy R(δ), pointer states via einselection, and spectrum broadcast structure (SBS) fidelity. The system achieves at most FSBS ≈ 0.20, far below the FSBS = 1.0 required for full quantum Darwinism, because the single-exciton subspace fundamentally limits the information per environmental fragment to less than 0.05 bits. The dominant pointer state eigenvalue (λ₁ = 0.31) confirms einselection is active, but the information redundancy is suppressed by the excitation number constraint. Pairwise quantum mutual information between the system and environment sites ranges from 0.42 to 0.73 bits (at t = 0.5 ps), with site 2 carrying the most information. These results demonstrate that photosynthetic complexes, while hosting rich quantum dynamics, are constrained by their single-exciton nature from achieving the full quantum Darwinism paradigm.
A study published on arXiv has strictly demonstrated the existence of true multipartite quantum entanglement between bacteriochlorophyll-a (BChl a) molecules within the Fenna-Matthews-Olson (FMO) light-harvesting complex of green sulfur bacteria. Using entanglement measures in the single-excitation subspace (bipartite concurrence and a global entanglement measure), the study proved for the first time in a biological system that these entanglement states persist for approximately 2 picoseconds (ps) not only at cryogenic temperatures but also at physiological temperatures (300 K, room temperature), surviving macroscopically. The findings suggest that strong quantum entanglement between distant molecules can enhance the robustness and efficiency of the energy transfer network as the exciton moves toward the reaction center, even amidst environmental noise (decohering effects). [Quantum Biology Society] Photosynthesis, known as one of the most efficient energy conversion processes in nature, has long been a subject of wonder for scientists. While previous research focused on quantum coherence at the single-particle level, a groundbreaking study has recently been published mathematically proving that "true quantum entanglement"—the non-local correlation between multiple pigment molecules—actually operates within living organisms, drawing global attention. The paper titled "Quantum entanglement in photosynthetic light harvesting complexes," published in the preprint repository arXiv, is evaluated as a monumental achievement in elucidating macroscopic quantum phenomena in biological systems. An international joint research team led by Mohan Sarovar, Akihito Ishizaki, Graham R. Fleming, and K. Birgitta Whaley from UC Berkeley and Lawrence Berkeley National Laboratory (LBNL) in the USA spearheaded this innovative research. ■ Demonstration of Multipartite Quantum Entanglement within the FMO Complex The researchers focused on the FMO (Fenna-Matthews-Olson) light-harvesting complex of green sulfur bacteria (Chlorobium tepidum). By precisely analyzing the exciton dynamics between the pigment molecules within the complex using a non-Markovian quantum master equation, they proved through bipartite concurrence and a measure of global entanglement that true multipartite quantum entanglement is formed, going beyond simple individual coherence. This marks the first rigorous instance of quantifying quantum entanglement in a biological system. ■ Quantum Information Maintained Through Room-Temperature Noise The most surprising discovery is that these delicate quantum entanglement states survive meaningfully even at warm and wet physiological temperatures. While it was generally thought that quantum states are instantly destroyed by the thermal fluctuations of the surrounding proteins and solvent (decohering effects), the study's results confirmed that the natural FMO complex maintains bipartite entanglement between dimerized pigments and even a small amount of long-range and multipartite entanglement at 300 K. This entanglement plays a crucial role in enhancing the efficiency and robustness of the energy transfer network as the exciton travels to the reaction center. ■ Living Organisms as Optimized Quantum Machines This study suggests that living organisms are not merely losing quantum phenomena in harsh environmental noise but are rather highly designed, optimized quantum machines that endure and actively utilize them. Mimicking these perfect energy transfer mechanisms of nature is expected to provide key physical clues for maximizing the efficiency of next-generation solar cells or developing innovative quantum communication and metrology devices that operate robustly even at room temperature. https://arxiv.org/abs/0905.3787
Abstract Quantum effects in photosynthetic energy transport in nature, especially for the typical Fenna-Matthews-Olson (FMO) complexes, are extensively studied in quantum biology. Such energy transport processes can be investigated as open quantum systems that blend the quantum coherence and environmental noise, and have been experimentally simulated on a few quantum devices. However, the existing experiments always lack a solid quantum simulation for the FMO energy transport due to their constraints to map a variety of issues in actual FMO complexes that have rich biological meanings. Here we successfully map the full coupling profile of the seven-site FMO structure by comprehensive characterisation and precise control of the evanescent coupling of the three-dimensional waveguide array. By applying a stochastic dynamical modulation on each waveguide, we introduce the base site energy and the dephasing term in coloured noise to faithfully simulate the power spectral density of the FMO complexes. We show our photonic model well interprets the phenomena including reorganisation energy, vibrational assistance, exciton transfer and energy localisation. We further experimentally demonstrate the existence of an optimal transport efficiency at certain dephasing strength, providing a window to closely investigate environment-assisted quantum transport.
Recently, long-lasting quantum effects in a number of photosynthetic complexes, which are pigment-protein molecular aggregates (PPMAs), were experimentally verified. These findings created an interest in trying to connect the known highly efficient excitation energy transfer (EET) in these systems to the existence of quantum effects such as quantum coherence and quantum correlations. It also raised the question of how these sensitive quantum effects can survive in such a macroscopic system. This thesis explores the existence and possible role of quantum effects in the EET in PPMAs. These systems can be modeled as non-Markovian open quantum systems and quantum effects can be investigated and quantified by methods developed in quantum information theory. Firstly, it is found that quantum nonlocal correlations in the EET in the Fenna-Matthews-Olson complex - a PPMA found in nature - are unlikely to exist when the initial excitation occurs in a natural manner. When the initial excitation occurs in an artificial manner by localization of the excitation on one pigment, nonlocal correlations exist on a short time scale. It is further found that in order for nonlocal correlations to be preserved in such a system, the excitation must be trapped on two pigments at the time and these pigments must not interact strongly with other pigments in the complex. Secondly, it is shown that quantum coherence is not in general a resource for efficient EET in model systems consisting of a network of pigments; systems optimized with respect to the amount of coherence do not coincide with systems with optimal EET efficiency between two end-site pigments. Thirdly, it is found that environmental effects and system-environment interactions can be tuned to optimize the EET efficiency in model PPMAs. The features of optimal environments highly depends on the structure of the pigment system and in particular, the relationship between the pigments excitation energies. It is further shown that a non-Markovian dynamics cannot be connected to an increased EET efficiency in these systems.
Abstract Near-unity energy transfer efficiency has been widely observed in natural photosynthetic complexes. This phenomenon has attracted broad interest from different fields, such as physics, biology, chemistry, and material science, as it may offer valuable insights into efficient solar-energy harvesting. Recently, quantum coherent effects have been discovered in photosynthetic light harvesting, and their potential role on energy transfer has seen the heated debate. Here, we perform an experimental quantum simulation of photosynthetic energy transfer using nuclear magnetic resonance (NMR). We show that an N-chromophore photosynthetic complex, with arbitrary structure and bath spectral density, can be effectively simulated by a system with log2N qubits. The computational cost of simulating such a system with a theoretical tool, like the hierarchical equation of motion, which is exponential in N, can be potentially reduced to requiring a just polynomial number of qubits N using NMR quantum simulation. The benefits of performing such quantum simulation in NMR are even greater when the spectral density is complex, as in natural photosynthetic complexes. These findings may shed light on quantum coherence in energy transfer and help to provide design principles for efficient artificial light harvesting.