From: sarfatti@well.sf.ca.us (Jack Sarfatti)
Subject: Photon pair Mach-Zehnder Interferometer IV
Organization: Whole Earth 'Lectronic Link
Date: Thu, 19 Nov 1992 08:20:42 GMT


Preamble:Ramsay's remarks about summing over phi are clearly wrong as he
has not conceptually distinguished between a 2-slit experiment and a Mach-
Zehnder experiment.

*Yes, if my transmitter used two slits and a screen, then Ramsay would be
right. But his point is not relevant for the Mach-Zehnder case.




#6 pair-correlated light (single transmitter counter |1>)


   |3>     _                   _
   -|-|-|-| |                 | |-|-|-|-|-|-\
          | |                 | |    |e+>   |
          | |                 | |           - (phi)
   |4>    | |                 | |    _      |
   -o-o-o-|_| <-    O       ->|_|-o-|_|-|-|-0 |1>

                                    1/2



   receiver                     transmitter


Fig. 6A

As before in #5:

The initial "entangled" (i.e. quantum-connected) photon-pair state is:

|a,b> = {|a,e>|a,+>|b,+> + |a,o>|a,->|b,->}/sqrt2

local unitary action of both phi-meter in e-path and 1/2 wave plate in o
path of photon a is "polarization disentanglement":

|a,b> -> {e^iphi|a,e>|a,+>|b,+> + |a,o>|a,+>|b,->}/sqrt2

       = |a,+>{e^iphi|a,e>|b,+> + |a,o>|b,->}/sqrt2 = |a,b>'

The recombination at counter 1 induces

|a,b>' -> |a,+>|1>{e^iphi|b,+> + |b,->}/sqrt2 = |a,b>'''

Ramsay and others object that no unitary transformation can make two
orthogonal states go to a single state in the sense that an orthogonal
basis cannot be collapsed to one vector in the basis. That is true, but
that is not what is happening here. What we have here is the time-reverse
of a beam splitter. For example in #1 an initial state |a> was split into
two orthogonal states |t> and |r>. That is:

|a> -> [|t> + i|r>]/sqrt2

clearly the time reverse is also possible

[|t> + i|r>]/sqrt2 -> |a>

This is not the same as |t> -> |t> and |r> -> |t> which is what I was
construed to have meant - partly my own fault, perhaps. But this is what I
mean now! In the case at hand, it not that

|a,e> -> |a,e> and |a,o> -> |a,e> but rather |a,b>' -> |a,b>'''

note that

<a,b|a,b> = '<a,b|a,b>' = '''<a,b|a,b>''' = 1

so these transformations are unitary.

Let us review:

|a,b> is entangled both in space and spin spaces. The half-wave plate
disentangles |a,b> in spin space to |a,b>'. The single counter arrangement,
which may require some clever optical engineering to construct properly,
further disentangles in space |a,b>' to |a,b>'''.

Indeed,

|a,b>''' = |a>|b> where

|a> = |a,+>|1>

|b> = {e^iphi|b,+> + |b,->}/sqrt2


Therefore, the phase information at the transmitter has been "teleported"
to the receiver on the quantum connection by the quantum erasure of both
the spin and space information at the transmitter. This is a new law of
physics buried in standard quantum mechanics.

p(3) = |<3|b>|^2 = |(e^iphi cos@ + sin@)/sqrt2|^2 =  [1 + sin2@ cos(phi)]/2

p(4) = |<4|b>|^2 = |(-e^iphi sin@ + cos@)/sqrt2|^2 = [1 - sin2@ cos(phi)]/2

p(3) + p(4) = 1

The quantum connection signal is

p(3) - p(4) = sin2@ cos(phi)

where @ is the nonlocal parameter - the difference in orientations of the
two crystals at the spacetime events in which each photon in the same pair
locally interacts with its crystal. The space-time interval between these
two events is irrelevant( which Budnik fails to understand in his wrong
"collapse or collapse" usenet posting).

Ramsay's remarks about summing over phi are clearly wrong as he has not
conceptually distinguished between a 2-slit experiment and a Mach-Zehnder
experiment.

*Yes, if my transmitter used two slits and a screen, then Ramsay would be
right. But his point is not relevant for the Mach-Zehnder case.





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