From: Lee Corbin (lcorbin@tsoft.com)
Date: Sat Sep 14 2002 - 10:42:33 MDT
scerir writes
> -----Original Message-----
> From: owner-extropians@extropy.org
> [mailto:owner-extropians@extropy.org]On Behalf Of scerir
> Sent: Thursday, September 12, 2002 7:38 AM
> > But to return to MWI again, probabilities there retain their
> > classical simplicity.
>
> In MWI? Difficult to normalize probabilities in there.
"In there"? The probabilities that I'm talking about are
those that simply arise in the laboratory when performing
any 1920's type calculation. If the new state can be any
one of a, b, c, then the classical probabilities are found
to be a^2, b^2, c^2 respectively, where these add up to 1.
Of course, for all I know, these could turn out to be
Bayesian probabilities ;-)
> But MWI is very useful anyway. Because it goes deeper.
> That is (perhaps, who knows) because QM is 'non-local'
> and the MWI is 'non-local' by definition: *many* worlds!
Not according to David Deutsch. Have you discussed this
with him on the FoR list, or read his book "The Fabric of
Reality"? As I recall, he adamantly denies that MWI is
non-local.
> The superposition principle requires non-local states.
I don't think so at all.
> Actually this kinematical non-local reality (i.e. entanglements)
> exists *before* any related local events (spatially separated)
> occur. In quantum teleportation a state has to be prepared
> initially. But after this preparation the state exists but it
> is at no place.
One would say (in MWI) that we're talking about the state of
the entire universe (or a part of it, anyway). Perhaps you
regard "locality" to mean something different; I think of it
as not requiring spooky influences at a distance (which is
incredibly uncomfortable to those to whom special relativity
has become second nature).
> Alice has photon 1, which is in a certain quantum state,
> unknown to Alice and unknown to anyone else.
> Let us say that this unknown quantum state is
> |psi>_1 = a |0>_1 + b |1>_1
> with |a|^2 + |b|^2 = 1
> and where |0>_1 and b |1>_1 represent two orthogonal quantum
> states and a and b represent complex amplitudes.
>
> Now Alice wants to *transfer* her quantum state to Bob,
> which is remote, so she can not directly deliver it to
> him. But, fortunately, Alice also has a pair of entangled
> photons, let us say the photon 2 and the photon 3, and she
> already gave the photon 3 to Bob, who still has
> this particle.
Yes, so far this is all easy.
> Leaving apart normalization factors we can write that the total state
> of those 3 photons is
> |psi>_1,2,3 =
> ( |0>_1 |1>_2 - |1>_1 |0>_2 ) (- a |0>_3 - b |1>_3 ) +
> ( |0>_1 |1>_2 + |1>_1 |0>_2 ) (- a |0>_3 + b |1>_3 ) +
> ( |0>_1 |0>_2 - |1>_1 |1>_2 ) ( a |1>_3 + b |0>_3 ) +
> ( |0>_1 |0>_2 + |1>_1 |1>_2 ) ( a |1>_3 - b |0>_3 )
Now that's a bit much (for me). This looks vaguely familiar
from those distant times that I've studied quantum teleportation,
but would you mind adding a word of explanation for the origin
or meaning of each of those eight factors? Each one is the
state of what? Or amplitude of what going to what? Thanks.
> Alice now performs a measurement on photons 1 and 2 and she
> projects her two photons onto *one* of these four states below:
> ( |0>_1 |1>_2 - |1>_1 |0>_2 )
> ( |0>_1 |1>_2 + |1>_1 |0>_2 )
> ( |0>_1 |0>_2 - |1>_1 |1>_2 )
> ( |0>_1 |0>_2 + |1>_1 |1>_2 )
>
> And consequently Bob will find his photon in *one* of these
> four states below
> (- a |0>_3 - b |1>_3 )
> (- a |0>_3 + b |1>_3 )
> ( a |1>_3 + b |0>_3 )
> ( a |1>_3 - b |0>_3 )
Your use of the word "consequently" worries me. One has to
suppose that Alice and Bob are in different galaxies separated
by billions of light years. In MWI (thanks for the analysis
below), one need not consider non-local "influences". It will
merely turn out that one version of Bob eventually discovers
himself to be in the same universe as the appropriate version
of Alice, and vice-versa.
> Now Alice, who wants to *transfer* the unknown quantum state of photon
> 1 to Bob, must inform Bob, via a classical channel, about her measurement
> (projection) result (on photons 1 and 2). So Bob can perform (25% of times
> it is not required) the right simple unitary transformation on his photon 3, in
> order to obtain the initial quantum state |psi>_1 = a |0>_1 + b |1>_1
>
> Note that Alice does not get any information, from her measurement, about
> the quantum state she wants to *transfer* and about the values of those
> a and b amplitudes. Note also that during Alice's measurement photon
> 1 loses his original quantum state, as required by the no-cloning theorem.
>
> Ok, that was the basic teleportation of a quantum state from Alice to Bob.
>
> Now something *very* strange happens in the MWI version. Alice's
> measurement does *not* project the superposition of
> ( |0>_1 |1>_2 - |1>_1 |0>_2 )
> ( |0>_1 |1>_2 + |1>_1 |0>_2 )
> ( |0>_1 |0>_2 - |1>_1 |1>_2 )
> ( |0>_1 |0>_2 + |1>_1 |1>_2 )
> onto just *one* of these quantum states (above). They *all* exist.
>
> And *all* these (Bob's) quantum states (below) also exist.
> (- a |0>_3 - b |1>_3 )
> (- a |0>_3 + b |1>_3 )
> ( a |1>_3 + b |0>_3 )
> ( a |1>_3 - b |0>_3 )
> and one of them (1 over 4 = 25% of times) is the same quantum state
> that Alice wanted to *transfer* to Bob. But it was *already* *there*.
As I say, I'll have to book up a bit to follow that, though
if you have the time to provide the earlier explanation that
I asked for, perhaps all this will become clear to me and
the rest of your readers.
But this does appear to be a very *nice* difference between
MWI and other interpretations. Our discussion may boil down
to why you consider this to be "very strange".
Lee
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