From: sarfatti@well.sf.ca.us (Jack Sarfatti)
Subject: QM Connection Communication Expt. re-visited.
Organization: Whole Earth 'Lectronic Link
Date: Wed, 27 Jan 1993 07:59:46 GMT


Quantum Connection Communication
I have been taking a fresh look at my gedankenexperiment to achieve quantum
connection communication by disentangling an entangled state. The three
mathematical considerations are linearity, orthogonality and unitarity. I
think that some of the initial objections by Gallis and others regarding
the nonlinearity of my scheme while apparently correct formally were
actually not ocrrect physically.

Here is the basic point regarding the linearity objection. In Fig.1,
imagine two Stern-Gerlach magnets. One splits the beam, the other
reconstructs the initial state.

               _________________ |+>__________________
  |i>         /                                       \              |i>
------------/                                           \_______________
            \                                           /
              \_________________ |->__________________/

Fig.1

|i> = |+><+|i> + |-><-|i>

<+|-> = 0

               ___________________ |+>______________
  |i>         /                                     \                |f>
------------/                                         \_________________
            \            __                           /
              \____|->__|U |______ e^i@|+> = U|->____/
                        |__|

Fig.2

In Fig.2, a spin-flip coil U is put in only one path. The second Stern-
Gerlach magnet is modified in design so that the two sub-beams are
recombined to one beam. This should be possible. I think a similar
experiment has actually been done with neutrons and neutron
interferometers. The output state |f> is no longer the same as the initial
state |i>. Assuming that the spin-flip does not correlate to orthogonal
number states of the radiation oscillator but, rather, to non-orthogonal
coherent Glauber states, we can write

|f> = |+><+|i> + U|-><-|i>

    = |+><+|i> + e^i@|+><-|i>

    = |+>[<+|i> + e^i@<-|i>]

<i|i> = <f|f> = 1  implies

<+|i><i|->e^-i@ + <-|i><i|+>e^i@ = 0

This is obviously physically correct, yet it "formally" appears to violate
linearity in that Gallis and others apparently insist upon wanting to write
that

|f>' = U|i> = U|+><+|i> + U|-><-|i> = e^i@(+)|-><+|i> + e^i@(-)|+><-|i>

which seems obviously physically wrong to me.

Now suppose we have an initial entangled pair state |1,2>, rather than the
above one-particle state |i>, in which

|1,2> = |1+>|2+><++|1,2> + |1->|2-><--|1,2>

Let the sender-photon 2 pass through the physical device of Fig 2, then if
I am right, the initial |1,2> is distorted to

|1,2>' = |1+>|2+><++|1,2> + |1->U(2)|2-><--|1,2>

       = |1+>|2+><++|1,2> + |1->e^i@|2+><--|1,2>

       = |2+>{|1+><++|1,2> + |1->e^i@<--|1,2>}

This means that the receiver photon |1> is polarized and its degree of
polarization depends upon both @ and also the mismatch & of the two
polarizers at each end which can, like @, be controlled from the sender.
The degree of polarization of photon |1> is controlled by real "telepathic"
action at a distance by the settings of the apparatus for twin photon |2>.
This would be quantum connection communication in which the locally
decodable message at the receiver is encoded by changing @ and & at the far
away sender. The physical reason for unitarity, conservation of probability
is clearly obeyed. Unlike the single photon case, @ is a free parameter.



From: ric@hpspdla.spd.HP.COM (Ric Peregrino)
Date: Thu, 21 Jan 1993 00:43:15 GMT
Subject: Re: Why only mass `distorts' space?
Organization: HP Stanford Park - Palo Alto, CA