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Someone sent me this link to a talk by Prof. Klaus Schulten from the University of Illinois: (my emphasis)

Quantum Computing and Animal Navigation

Quantum computing is all the rage nowadays. But this type of computing may have been discovered and used by living cells billion of years ago. Nowadays migratory birds use a protein, Cryptochrome, which absorbs weak blue light to produce two quantum-entangled electrons in the protein, which by monitoring the earth's magnetic field, allows birds to navigate even in bad weather and wind conditions. The lecture tells the story of this discovery, starting with chemical test tube experiments and ending in the demonstration that the navigational compass is in the eyes and can be affected by radio antennas. The story involves theoretical physicists who got their first paper rejected as "garbage", million dollar laser experiments by physical chemists to measure the entangled electrons, and ornithologists who try to 'interrogate' the birds themselves. This work opens up the awesome possibility that room-temperature quantum mechanics may be crucial in many biological systems.

Now here's my question: What's the big deal with entangled electrons? I mean, if I do not neglect electron-electron interaction, then pretty much all electrons in a condensed matter system are entangled, are they not? Electrons in the same angular momentum multiplet are entangled via Hund's rule, electrons on neighboring sites in a tight-binding (or, in the interacting case, Hubbard) model can all be entangled due to an antiferromagnetic exchange coupling, etc. etc.

Sure, for a quantum computer I'd like to have physically separated electrons maintain their entanglement, and I'd like to have fine-grained control over which of the electrons are entangled in which way etc, but for chemical processes in molecules such as these earth-magnetic-field receptors, is it not a bit sensationalist to liken such a process to quantum computing?

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Reminds me of a talk I went to about how the electronic energy transfer in photosynthesis (photosystem II supercomplex) is quantum coherent. There was a lot of sensationalism in that too, but also real science. – Keenan Pepper Apr 12 '11 at 4:37
Sensationalism is exactly the word I'm thinking of, although I don't feel like I'm in a position to criticize the work mentioned above. That's why I'm asking :) – Lagerbaer Apr 12 '11 at 4:43
This is sociology; the all other quantum phenomena (even more complex) happening there can be just called "chemistry" which is not that jazzy. – mbq Apr 12 '11 at 7:04
up vote 6 down vote accepted

I think the issue is we need to separate the 'expected'/obvious quantum effects, from the unexpected ones. For instance, some of your questions refer to quantum mechanics in molecular structure. In the most trivial sense, we couldn't even have molecular structure or even stable atoms if $\hbar \rightarrow 0$ such that there are no quantum effects. So in a trivial sense, every protein structure is due to quantum mechanics. Following up on this...

I mean, if I do not neglect electron-electron interaction, then pretty much all electrons in a condensed matter system are entangled, are they not?

Yes. In the simplest picture of matter, chemists refer to electrons occupying molecular orbitals. This is the Hartee-Fock approximation in quantum chemistry, and since the wavefunction is written as a slater determinant of the occupied molecular orbitals, in this approximation there is no electron-electron position correlation. Obviously in the real world this is not the case. The wavefunction will be correlated to have two electrons further apart on average than in the simplified molecular orbital picture. This means the state is not a product state and there is indeed entanglement of the electron positions. So you are correct on this.

(And as an aside, more advanced multi-electron computational methods beyond Hartree-Fock can of course be used to account for most of this correlation energy in theoretical calculations. The molecular orbit picture works very well though, which is why this is how it is introduced to students and how chemists colloquially discuss and visualize the quantum mechanics of a molecule.)

However, again this is in some sense the 'trivial' effects of quantum mechanics, as it is just "chemistry". But as we get to larger structures, due to interaction with the environment and decoherence, we can increasingly well describe everything with phenomenological parameters and a classical theory. True the phenomenological parameters are due to the quantum mechanics, but this is not the exciting part.

The exciting part is when we can't describe the protein interactions with phenomenological models due to the quantum coherence playing an important part at the macroscopic level.

Yes, it is somewhat arbitrary where we draw this line. But few really thought biology would end up using something so fragile as the coherence of entangled states to actually improve biological function. The better studied example I've seen regarding this is energy transfer in a particular photosynthesis step.

Whether something is amazing or not isn't really a scientific question, but hopefully I clarified enough regarding your question of entanglement of electrons in molecules to see how the use of coherence to improve biological function is at the least unexpected, and hopefully exciting to you as well.

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What's the big deal with entangled electrons?

If you had even mentioned the possibility that entanglement would play any role in biological systems, ten years ago or so you would have been greeted with eye-rolling and finger-wagging. Fortunately since then we have become accustomed to seeing mentions of "entanglement" all over the place. This is justifiably so. Entanglement is a new resource, much as coal, oil or nuclear power were at one point in history, that holds almost unlimited possibilities.

I mean, if I do not neglect electron-electron interaction, then pretty much all electrons in a condensed matter system are entangled, are they not?

No. Not in general. Entanglement is, of course, present in any many-body quantum system to some extent. One example where this is quite explicit is in some proposed mechanisms of high-T_c superconductivity built around the the Resonance Valence Bond (RVB) state [see this question on physics.SE and the accompanying answer] where the "valence bond" between two neighboring spins is nothing more than a spin-singlet entangled bell state:

$$ |\Psi\rangle = \frac{1}{\sqrt{2}}\left( |\uparrow\rangle |\downarrow\rangle - |\downarrow\rangle |\uparrow\rangle \right) $$

This is an example of bipartite entanglement, i.e. entanglement between two subsystems. In general one can have *multi*partite engtanglement between $N$ number of quantum systems. Again, the presence of bipartite or pairwise entanglement in a RVB state or due to the sort that lead to a contribution of the specific heat of a material (ref:Sondhi et al.), does not imply by any means that "all electrons are entangled". I hope this point is very clear.

Entanglement on large-scales (i.e. scales comparable to the size of the system itself, only then can you justify the statement that "all the particles" in a system are entangled) is a non-generic phenomenon that is a signature of so-called quantum phase transitions. It has been suggested [for references and background see the RMP by the Horodecki clan - in particular col. 2 first para. page 4.] that the entanglement entropy of any susbsystem with the rest of the system diverges near a quantum phase transition and can considered (see for eg. Levin and Wen, PRL, 2006 and Kitaev and Preskill, PRL, 2006) as an order parameter for characterizing topological phases.

To sum, (AFAIK) it is only near the critical point associated with a quantum phase transition (when the entanglement entropy of a "test" subsystem diverges) where all subsystems of the given system can be said to be entangled with all other subsystems thus justifying the phrase "all electrons ... are entangled".

[Nb: See also remarks on entanglement in the Slater determinant state at the end of this answer.]

The presence of entanglement in 1D spin-chains and such might be ubiquitous but its presence in the (approx.) 1D biomolecular chains such as DNA, RNA and various proteins would certainly be nothing less than extraordinary.

If entanglement is actively exploited in any biological processes - avian navigation, photosynthesis or others - the implications for biology are phenomenal. We've already seen what evolution has managed to come up with as far as nano-technology (ATP synthesis, bacterial navigation, myosin motors, etc.) and command-and-control systems (nervous system, endocrine system, etc.) are concerned. What more can be explained by throwing entanglement into the mix?

Sure, for a quantum computer I'd like to have physically separated electrons maintain their entanglement, and I'd like to have fine-grained control over which of the electrons are entangled in which way etc, but for chemical processes in molecules such as these earth-magnetic-field receptors, is it not a bit sensationalist to liken such a process to quantum computing? [emph. mine]

Perhaps a little but the enthusiasm is understandable. First of all the greatest challenge of quantum computing is to be able to design systems that do not lose their entanglement due to decoherence. For this generally one tries to keep the system at low temperatures. But it would not be feasible for a biological system which operates at room temperatures and above to maintain sub-zero temperature. Despite this obstacle, the fact that quantum systems stable against decoherence already exist in the warmest, slushiest of all regimes - biology - is therefore a big shock.

You might still say that comparing the situation to a quantum computer is a bit of a stretch. Then again what lengths will people go to in order to attract the funding agencies' good graces?

The cryptochrome, at its most basic, is a detection device such as a Geiger counter. On its own a single such device does not constitute a circuit, per se. The question is: do biological systems utilize quantum computation in a non-trivial manner? (i.e. with circuits which perform a more complex computation than just the detection of the direction of a magnetic field).

PS: The answer by @Edward appears to suggest that the Slater determinant state is a de facto entangled state. If this was the case then any (even a non-interacting) many-body fermionic system would be considered entangled. There is the suggestion (T.A. Kaplan) that according to the traditional definition of entanglement as being present in any non-factorizable state, the Slater determinant should be considered entangled. However, the notion of entanglement as discussed in Shi, Wang & Kais and Schliemann, Loss & MacDonald explicitly rules out consideration of the Slate state as a a measure of entanglement.

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Well, in fact the justified function of cytochromes is being an electron temporary storage and "housing" in redox reactions; only CYPs mess with light, but are not known of detecting anything. And we know a (quite classic) biological mechanism of detecting magnetic field -- the magnetosomes. There is even a paper about finding them in pigeons before this quantum computing rush. – mbq Apr 12 '11 at 7:28
@Deepak "No. Not unless you're near a critical point." Can you expand on this? Electron-electron interactions, if not neglected, should yield a finite correlation energy. – Edward Apr 12 '11 at 7:33
@mbq - thanks for those links. @Edward - that was a hastily written phrase. My own answer to this question would appear to give a counter example with the work of Ghosh et al. Thanks for pointing this out. – user346 Apr 12 '11 at 9:09
On third thoughts I did have a strong intuition for my statement that (large-scale) entanglement occurs only near a critical point. I have tried to explain why this is the case in the most recent edit. I hope readers will find this explanation satisfactory or at the very least intriguing. – user346 Apr 15 '11 at 13:54

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