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From: scerir <scerir.domain.name.hidden>

Date: Wed, 10 Jul 2002 23:00:29 +0200

*> 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] :-)

Received on Wed Jul 10 2002 - 13:58:20 PDT

Date: Wed, 10 Jul 2002 23:00:29 +0200

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] :-)

Received on Wed Jul 10 2002 - 13:58:20 PDT

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