First, I correct something I said in my previous post. Contrary to what I said, delocalised one exciton states can be entangled. For example consider 2 chromophores and one exciton

delocalised between them

|psi> = |01>+|10>

where |01> denotes the first chromophore in its ground state and the second chromophore in its excited state. This state actually has maximum entanglement. Hence, a Bell type experiment could establish entanglement between chromophores. However, is this entanglement relevant for functionality in photosynthesis, as claimed by Fleming's group? Specifically, in their Nature paper they speculate that the protein may perform a quantum computation analogous to Grovers algorithm to find the most effecient way to channel the exciton.

Nein! Here is a simple physical argument. Quantum information processing achieves exponential speed up by making use of the complete Hilbert space.

If we have N chromophores, the size of the complete exciton Hilbert space is 2^N. The one exciton sector is a small part of the whole Hilbert space. For example, for the 7 chromophores in the FMO complex it comprises 7/1024 (i.e., less than 1 per cent) of the whole Hilbert space.

If the plant did a quantum computation to decide how to channel the exciton from chromophore A to B it would have to be exploring multiple exciton states. But such states have energies which are comparable to optical photon frequencies and thus orders of magnitude larger than the energy scales associated with fluctuations in the environment and the interactions between the chromophores.

These delocalised exciton states are completely analogous to the Bloch one electron states which occur in crystals (such as silicon). But I don't think quantum information is relevant to understanding solid state physics and devices.

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Hi Ross,

ReplyDeleteI completely agree with this. And the argument you gave about Grover's search needing an exponentially scaling Hilbert space is fine as an objection. But we recently got to thinking that one could think of a variant of Grover's search where a unary encoding is used and an advantage over classical search is gained by exploring the (exponentially many) sites faster using quantum dynamics. This would not be an space efficient implementation, but perhaps one could talk about a quantum speedup being used to advantage by light harvesting complexes. But (alas) this is also not the case either, and we have recently shown this rigorously. If you're interested, see: arXiv:0910.1847 [quant-ph]. It turns out that the very features that are crucial to light harvesting in LHCs, also lead to sub-diffusive transport (i.e. no quantum speedup) at all except very short times.

~mohan