Hi Serafino,
At 23:00 +0200 10/07/2002, scerir wrote:
> > Hal
>> You can also have a "block universe" in QM with the many-world
>> interpretation. It has a more complicated geometric structure but
>> philosophically it is deterministic, with the same issues regarding
>> changes, free will, etc.
>
>I'm not an Everettista, anyway let us try. 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" (I say: "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.
>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 )
>
>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 found 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 )
>
>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 (= trasportation) of a quantum state from
>Alice to Bob.
>
>Now something 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
>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.
>
>Thus it seems that in the MWI of teleportation the quantun state it is not
>"teleported" or "trasported" but it is already "there", and it is already
>"there", in one of those branches, from the beginning. This stuff
>reminds me of
>the "block universe", at least a bit.
>
>s.
>
>[still not an Everettista] :-)
Still not? Even after this nice presentation of (quantum) teleportation
in the MW view? Your last remark confirms my feeling that quantum information
is "just" classical information about which partition of the multiverse
we belong (and measurement is always sort of self-localisation).
Do you know the paper by Peres
http://xxx.lanl.gov/abs/quant-ph/9904042
Peres shows how to teleport entanglement in the past! In the MW view there
is no problem at all, neither non-locality, nor 3-indeterminacy. But Peres
concludes its paper by insisting on keeping the Copenhague view. It's
quite mysterious.
If you have time to look at it I would appreciate your opinion.
Bruno
Received on Fri Jul 12 2002 - 03:41:04 PDT