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The non-orthogonal LCAO orbitals may play a role there.
Scientists have further realized that the Kondo effect results from a relationship between electrons known as "entanglement" in which the quantum state of one electron is tied to those of neighboring electrons, even if the particles are later separated by considerable distances. In the case of Kondo effect, a trapped electron is entangled in a complex manner with a cloud of surrounding electrons.
Researchers have been intrigued by the Kondo effect in part because understanding how a trapped electron becomes entangled with its environment could help overcome barriers to quantum computing, which could lead to far more powerful computers than currently exist.

When I was at UCSD with the Benford brothers in the late 60's Walter Kohn and Harry Suhl were very interested in the Kondo effect. Too bad the connection to entanglement was not understood back then. Also in photosynthesis and no doubt many biological processes.
On Jul 3, 2011, at 9:56 PM, JACK SARFATTI wrote:
this one looks most relevant
On the possibility to use non-orthogonal orbitals for Density Matrix Renormalization Group calculations in Quantum Chemistry
A. O. Mitrushenkov, Guido Fano, Roberto Linguerri, Paolo Palmieri
(Submitted on 3 Jun 2003)
The generalization of Density Matrix Renormalization Group (DMRG) approach as implemented in quantum chemistry, to the case of non-orthogonal orbitals is carefully analyzed. This generalization is attractive from the physical point of view since it allows a better localization of the orbitals. The possible implementation difficulties and drawbacks are estimated. General formulae for hamiltonian matrix elements useful in DMRG calculations are given.
Comments:    14 pages
Subjects:    Strongly Correlated Electrons (cond-mat.str-el)
Cite as:    arXiv:cond-mat/0306058v1 [cond-mat.str-el]
Submission history
From: Roberto Linguerri [view email]
[v1] Tue, 3 Jun 2003 10:02:27 GMT (15kb)

However, none of them directly address our problem of entanglement signals. However, if these non-orthogonal LCAO orbitals are physically significant it might explain the nonlocal effects in photosynthesis and I bet in many complex systems not in thermodynamic equilibrium as entanglement signaling? Also Hameroff's microtubules etc.
On Jul 3, 2011, at 4:34 PM, Paul Zielinski wrote:
Much recent work has been done in atomic and molecular physics with a density matrix formalism using non-orthogonal bases. This includes strongly correlated density matrices with spacelike-separated supports. So I don't think there is anything new or strange here.
However, naively speaking it seems to me that if the trace of a density matrix, or of the product of a density matrix and an "observable", is only invariant under unitary transformations, then applying a non-unitary transformation to get from an orthogonal basis to a non- orthogonal basis representation necessarily changes the physical meaning of the trace.
Isn't that what Kastner is saying here? How do you answer that?

Simple, I only claimed that the initial choice of a non-orthogonal basis is preserved under unitary transformations. I never invoked a non-unitary transformation from an orthogonal to a non-orthogonal basis, though that is also of interest. It is another story.
On 7/3/2011 4:13 PM, Jack Sarfatti wrote:
No I don't think it's that simple. Sure, if you use spins then the eigenstates are orthogonal and no FTL signal. We all agree on that. Simply because we maybe cannot do it with polarization entanglements does not mean we can't do it with other degrees of freedom.
The Glauber states are a different story. Suppose mean n i.e. is small order of 1 or 2
z = ^1/2e^i@
the point is that there is coherence between the vacuum |0>, and all states |1>, |2> ....
but the peak is at with a Poisson distribution. The coherence properties are qualitatively different from that of a sharp n Fock state - though not so different when is small agreed.
Even when >> 1 it is a mistake to think of it as a classical EM wave in the sense of Maxwell theory prior to laser beams.
I think Roy Glauber's original papers explain why. I need to refresh my memory on this from the 1960's.
Coherent microwaves are close to Glauber states, but not ordinary optical sources that are not lasers.
Glauber states and their squeezed variations have properties above and beyond their non-laser cousins e.g. from an incandescent lamp etc.
From: Ruth Elinor Kastner To: Jack Sarfatti Sent: Sun, July 3, 2011 12:38:36 PM
Subject: RE: The issue of small n
RK: OK then the issue is just the non-orthogonality itself ; this yields apparent FTL signalling trivially in cases
where we're pretty sure it can't be done.
JS:  All you sort of showed was that there was allegedly no way to prepare an over-complete basis of spin states of sharp n. Lasers show how to prepare many-photon states as Glauber states all with same polarization. The issue is then how they can entangle. Can we entangle laser beams with opposite momenta Fourier components as in the original EPR all with same polarizations? That's what I assumed in the toy model.
From: Jack Sarfatti [This email address is being protected from spambots. You need JavaScript enabled to view it.]
Sent: Sunday, July 03, 2011 3:00 PM
To: Ruth Elinor Kastner
Cc: nick herbert; david kaiser; Saul-Paul Sirag
Subject: The issue of small n
Assuming I did not make an error:
Large is not needed
Even small works in principle, though perhaps with a much smaller signal to noise ratio?
If there is large n then only the constructive peaks contribute to the non-orthogonality
If n is small then more relative phases @ contribute
= e^-(1-cos@(x'))   
this formula of mine may be wrong, I am not sure. It has nice properties however as a comb of Dirac delta functions when ---> infinity at @ = integer multiples of 2pi (constructive interference of the Young double slit fringes).
= x' integral over the screen of we also need
= x' integral over the screen of e^i@(x)
On Jul 3, 2011, at 9:03 AM, Ruth Elinor Kastner wrote:
RK: Hi all, I was just addressing the point stressed by Jack about using a non-orthonormal basis to compute the partial trace, since that's crucial to Jack's goal of obtaining a nonlocal signal. This is independent of whether or not there's a detailed picture of the experimental apparatus. I just take it as a conceptual thought experiment.
JS: Exactly. For some reason Nick Herbert took umbrage at that.
RK: The point is that if you allow partial trace to be done in a non-orthonormal basis you can get trivial nonlocal signalling in an ordinary EPR -spin experiment. So the question is whether using a nonorthonormal basis has any genuine physical application -- which seems doubtful, but the point is that IF you could use such states for your experiment, and maintain the entanglement you apparently get nonlocal signalling. It appears to me from at least one of the refs Jack sent on entangled coherent states that the entanglement depends on having a very small avg photon number (< or = 2) so that the partial trace does not depart from the standard def., and that one cannot use those for nonlocal signalling (which in Jack's analysis requires large avg photon mumber). Again I think the crucial point is that large n coherent states approximate classical waves which can't be entangled at the individual photon level. I would love to try to work this out quantitatively but too busy right now...
JS: It's too simple to say large means classical waves. That's like saying the superfluid is a giant classical wave. In other words there is a distinction between macro-quantum coherent waves and             classical waves of the same that shows up in the coherence correlation functions e.g. see modern books on quantum optics (or even Wikipedia).
In any case we agree this is a valid question that deserves careful investigation. I am not aware if any such work has been done?

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