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.
This post imported from StackExchange Physics at 2014-04-01 16:45 (UCT), posted by SE-user user346
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