# Reeh–Schlieder theorem in QFT and entanglement in biological systems

Context: There have been a few papers out recently which mention how photosynthesis in plants might have connections to entanglement, or even perhaps that entanglement is causing photosynthetic complexes to capture the sunlight and go through the conversion stages. Here are two papers worth mentioning:

Quantum oscillatory exciton migration in photosynthetic reaction centers.

Quantum entanglement between the electron clouds of nucleic acids in DNA

Question: In QFT, the Reeh–Schlieder theorem is thought to be an analogue of some sense to quantum entanglement. My question is that can one use the Reeh–Schlieder theorem instead of entanglement and try to do the work the other papers mentioned above have done but in a QFT context? To what extent does that analogue relationship hold? In that sense it is usable as a dual description under certain constrains?

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Uh, why do you think R-S is an analogue of entanglement? The only similarity I can see is that both produce some sort of non-locality. Entanglement gives more correlation than is classically possible (which then naively seems to imply action at a distance) while R-S tells you that arbitrarily small neighborhood in QFT knows about everything that goes on anywhere (formally, the set spanned by local operators on that neighborhood acting on a vacuum is dense in the whole Hilbert space of states). This is important because it gives operator-state correspondence. –  Marek Aug 17 '11 at 6:47

The concept of entanglement still applies in QFT. What the Reeh-Schlieder theorem tells you is that there is entanglement in the QFT vacuum state. So I take the question to be asking whether we could use the methods employed in proving the theorem, to decide that there is entanglement in biological systems. It seems possible, though first you have to find a biological system that you can describe in terms of quantum field theory. Let's take a much-hyped example, the microtubule. Just for argument's sake, suppose that one of the various possibilities listed in this paper made sense, and that there was an effective field theory describing the dynamics of delocalized electrons in the shell of the microtubule. Then maybe you could try to prove the Reeh-Schlieder property for the ground state of that effective theory at biological temperatures, along these lines.

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thanks Mitchell. –  dhillonv10 Aug 17 '11 at 20:00

As an aside, Dr. Stuart Hameroff discusses photosynthesis and quantum coherence on 'Singularity 1 on 1' at this link:

Regarding the Reeh–Schlieder theorem (1961), I note "it is subject to some doubt whether the Reeh–Schlieder theorem can usefully be seen as the quantum field theory analog to quantum entanglement, since the exponentially-increasing energy needed for long range actions will prohibit any macroscopic effects." - Wikipedia

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