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However, there appears to be a serious error in the key eq 16, which I think also applies to Leibfried’s eq. 146 as well. I am checking it carefully and will write it up with Math Type in proper notation.

Eq. 16 has

Pg(alpha,phi) = <S+|S+>

which is obvious nonsense since

<S+|S+> = 1 for Glauber coherent states.

I now not even sure if their final expression is correct.

The entangled state is Gerry’s eq 13 (attached pdf)

| PSI> = |alpha, phi;e,g> = |g>|S+> + |e>|S->

|S+,-> = (1/2)[|alphae^iphi/2> +- |alphae^0iphi/2>]

alpha is real

The phase phi MODULATION entanglement signal parameter is easily controlled precisely with the effective interaction Hamiltonian of eq. 9. So is the AMPLITUDE MODULATION entanglement signal parameter (real alpha). So we have choice of both PM and AM for messages - although in this case the sender and receiver are different degrees of freedom on the same ion, that will not always be so for more clever "total experimental arrangements" (Bohr)

Now something that a lot of Pundits don’t seem to know is that the usual prescription for the Born probability rule only works for orthogonal base states in the presence of entanglement!

The correct general way to compute responses is the one used by Stapp - the method of projection operators. This only works for STRONG VON NEUMANN measurements, not for pre & post-selected WEAK MEASUREMENTS. I only do the former here and will work on the latter when I get to London next week.

Following Stapp

1. form the total entangled Dirac KET-BRA projection operator

|PSI><PSI| = (|g><g|)(|S+><S+|) + three other terms

2. The STAND-ALONE LOCAL response function P(g) to detect the RECEIVER Jaynes-Cummings internal qubit in its ground state |g> is,

Gospel according to Stapp ;-)

Trace over all sender base states of |g><g| multiplied into |PSI><PSI|

Here is where the DISTINGUISHABLE NON-ORTHOGONALITY of the Glauber MACRO-QUANTUM COHERENT states make the crucial difference completely refuting all NO ENTANGLEMENT-SIGNAL PROOFS!

Remember Glauber coherent states are P.W. Anderson “More is different" emergent from spontaneous broken ground state symmetry (in this case U1 super-selection rule for particle number conjugate to phase) of complex systems, e.g. in a non-equilibirum laser above threshold or in an (thermal) equilibrium superconductor below phase transition critical temperature, or in a thermal equlibirium crystal, ferromagnet etc. etc.

Note the square of |g><g| is itself (idempotent)

The required trace is

P(g) = <g|{(|g><g|)(<S+|S+><S+|S+>) + (|g><g|)(<S-|S+><S+|S->)}|g>

= 1 + |<S+|S->|^2

The ANOMALOUS ENTANGLEMENT SIGNAL TERM is obviously  |<S+|S->|^2  that is zero in micro-quantum entangled states.

The Born probability rule is obviously violated since

P(e) = P(g)

P(e) + P(g) > 1

In Bohm’s theory, the probability rule is not an absolute truth of Copenhagen Church.

Therefore, the RECEIVER response functions P(e) and P(g) depend on the SENDER controllable settings alpha and phi in blatant violation of the No-Signal Theorems.


On Mar 24, 2012, at 10:47 AM, nick herbert wrote:

Jack--

Thanks for the review paper on "Quantum Dynamics of Single Trapped Ions" (henceforth LBMW). I am amazed
how much quantum behavior one can demonstrate with such a simple system. The trapped ion is essentially
a pocket demo of almost all of the effects you read about in quantum textbooks. I used to think that quantum
optics was the royal road to experiencing quantum weirdness firsthand. Now I am ceding second place to
trapped ion physics. I especially like the opening quote by Schrödinger that we will never be able to do experiments
on single atoms. LBMW show that not only are we able to do such experiments, but we can probe the quantum behavior
of a single atom to an astonishing degree of sophistication. And we can even SEE SINGLE IONS with the naked eye
due to laser induced fluorescence.

This intensity of this fluorescence is the signal of the interference experiment you are so excited about.

This is a very complicated experiment and I'm not sure I understand it completely but my take on it is that
you have misunderstood the nature of "phi". In terms of an analogous EPR experiment "phi" would not
be under the control of Alice or Bob but is merely a parameter controlled at the SOURCE of the EPR
pair--hence useless for signalling.

What happens in the experiment you cite from LBMW is that the experimenters set up a coherent state interference
experiment for one value of "phi". Then they set up a new experiment with a different value of "phi". Interference
between two motional states is revealed cause the motional states are entangled with the ground |g> and excited |e>
states. The phase is controlled by a series of set up pulses that operate on both the motion and the internal states--
hence the analogy with the EPR SOURCE rather than the EPR SIGNAL. These pulses are chosen initially to make the
fluorescence signal vanish--which happens when the |e> state is unoccupied.

The experimenters start with a superposition of two coherent motion states of fixed N and fixed phase difference "phi" which
are entangled with two internal states. They do an interference experiment (I'm not quite sure how this is carried out)
and measure the amount of |e>. then they do another experiment with different phi.

Again it seems to me that each value of phi corresponds to an entirely new EPR experiment. it is as if Clauser would change his EPR light source  and run the experiment again. The results will of course be different at Bob and Alice's stations and Clauser could send them signals. But this effect  is useless for sending a signal from Bob to Alice.

Thanks for drawing this experiment to my attention. I am impressed by its subtlety. But I see no way that it can be adapted
to FTL signalling. If you see such possibilities--by all means take the ball and run with it.

You may find some inspiration for your quest in the following entangled coherent state review article by Sanders

http://lanl.arxiv.org/abs/1112.1778

I am amazed that the person that discovered coherent states was Schrödinger!!!!! This was long before quantum field theory and Fock (number states). Even before the Born
probability interpretation for the wave function!!!! I wonder how he came to conceive of such a modern notion.. What was his motivation?

Thanks again for the LBMW paper. It taught me a lot about quantum theory and experiment.

Nick Herbert
http://quantumtantra.blogspot.com



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