## Teleportation

### Questions:

1. What is Entanglement ?
2. How do you prove Entanglement ?
3. What is the most difficult part related to quantum mechanical experiments ?
4. What is Teleportation ?
5. How do you prove Teleportation ?
6. Is it possible to demonstrate Teleportation in slow motion.
7. What is "Spooky action at a distance" ?
8. What is Locality versus Non-Locality

### Purpose

The purpose of the above first three questions is to investigate the physical significance of each.

### Answer question 1: What is Entanglement

In many processes particles are created. For example in processes were particles collide.
In most cases, specific were all the particles involved are different, there exists no relation between the different particles involved
But in some cases this is not, specific were the particles created are identical. For example two electrons or two photons.
• In the case of two electrons there can be a relation between the spin of each elektron. Spin is like an arrow. An arrow has a direction in space like: x,y and z.
If there is a relation between the spins, then it could be something like: If one has a direction like +x,+y and +z than the other one has the opposite direction i.e. -x,-y and -z.
• In the case of two photons there can be a relation between the plane of polarisation of each photon.
If there is a relation between those planes than the angle between those planes can be zero or 90 degrees.

### Answer question 2: How do you prove Entanglement

The only way to prove entanglement is by performing experiments.
The main tool to prove entanglement is by using a filter
In the case of a photon we assume the following configuration:
```              +y     F1    +Z
.   . |   .
. .   | .
.     |
. .   . |
.   . .   |
-x......F2..........F4...........> +x
|   . .   .
| .   . .
|     .
. |   . .
.   | .   .
.     F3    .
-z           -y
```
In the above sketch there is a photon which moves from left to right from -x to +x
There is a filter in the vertical -z,-y,+y and +z plane identified by the four letters F
The direction of the fiter is in the axis -z,+z. That means the angle between the direction of the filter and the horizontal plane -x,-z,+z and +x is zero.
• If the direction of the polarisation of the photon is also -x,-z,+z and +x than the photon will pass the filter and be counted.
• If the direction of the polarisation of the photon is also -x,-y,+y and +x than the photon will be absorbed by the filter.
To explain the same slightly different:
The direction of the polarisation plane of the photon has a certain angle with the plane -x,-z,+z and +x.
This angle is called alpha.
• When alpha is zero the photon passes.
• When alpha is 90 degrees the photon is absorbed.

However this is not the full picture:

• the photon passes when the angle is between -45 and 45 degrees including 0 degrees.
• the photon is absorbed when the angle is between 45 and 135 degrees including 90 degrees.
In reality this means if you know that you have one photon, but you do not know what the polarisation angle is than you have a 50% chance that the photon will pass and a 50% that the photon will be absorbed.

For more questions and photon pairs See: Experiments with Entangled photons

### Answer question 3: Which are the pratical problems ?

As discussed above when you study entanglement and photons then filters are used.
Depending about the polarisation plane of the photon and the filter angle there is a 50% that the photon will pass and a 50% chance that the photon will be absorbed
Be carefull this is a theoretical value, you have to perform experiments to prove that.
It is relative easy that a photon passes the filter, because you use a counter. Each increment tells you that you have at least one photon.
It is much more difficult to decide that a photon is absorbed.
There are two ways to improve that.
1. First you can use a two way analyser instead of a one way analyser. In a two way analyser no absorbtion takes place. A two way analyser is like a beam splitter. If the polarisation plane of is in the direction of the analyser (Plus or minus 45 degrees) the photon goes "left" otherwise the photon goes "right". Both beams can be counted.
2. By using a "Coincidence Monitor" or CM. A CM allows you to compare the sequences of events (increments) at each counter. As such you can conclude at each stream which photons are missing.
From an information point of view it should not matter if you are using a one or a two way annalyser. Ofcourse actual experiments should demonstrate if the two give exactly the same results.

### Answer question 4: What is Teleportation

When you discuss Teleportation starting point is always (that when you study photons) that you have photon pairs and that the photons in each pair are correlated.
The assumption is that this physical correlation is very strong and can be felt miles away.
In effect it is so strong that:
• if you change the state of one other should change also
• also if photon A (of a photon pair) is in state +a and photon B in state -a than if you change A from +a to -a than B should change from -a to +a.
• also if you know that you have two photons A and B which are correlated such that they move in same polarisation plane that when you change the polarisation angle of A that than B also should change in the same direction with the same angle.

### Answer question 5: How do you prove Teleportation

When you want to demonstrate Teleportation you have to be carefull about different issues:
1. First your experiment has to be asymetrical. You have a sending site and receiving site.
The sending site changes the state (of photon A). The receiving site should detect this state change (of photon B).
2. The sending site should not directly influence the receiving site.

The easiest way to prove Teleportation is as follows:

1. First you demonstrate that you have entangled photon pairs.
Such an experiment consists of a source, two counters (a certain equal distance away) and a coincidence monitor. There are no filters involved.
You perform this test for a certain duration and the result should be that the counts of each counter should be almost identical
The coincidence monitor should give the same result. For more detail See:
Experiment 1 with Entangled photons
2. Secondly, you repeat the same experiment (no changes to the source, no filters) for the same duration. Except for a small duration you place a screen before the left counter.
3. The result should be at least less counts on counter 1 but also less counts on counter 2 (if there is teleportation involved).
The same you should also see on the results of the Coincidence Monitor.

However you can also demonstrate Teleportation using two filters. See: Experiment 3 with Entangled photons The assumption is that both photons in each pair are polarised in the same plane. That means the angle between each photon pair is zero.
But also let us make an extra assumption: That the polarisation plane of each photon is zero.

1. First you perform the experiment exactly as described (same distance analysers) for a certain duration.
The result should be that counter 1 and 2 (+ direction) should be close to 100% of the total number of events.
The result for Counter 3 and 4 (- direction) should be each close to 0%
2. Next you repeat the same experiment but you move the left analyser 50% closer to the source.
The idea behind this change is to make the experiment asymetrical and "to measure" the left stream first.
The results should be the same.
3. You repeat the same experiment, (asymetrical setup) but slowly during the experiment you change the angle of analyser 1, forward and backward to zero.
4. This should have an effect on counter 1 and 3. Counter 1 should be less than 100% (for example 70%) and counter 3 should have more (in that case 30%)
5. If there teleportation involved (by the left sending side) the results of counter 2 and 4 should also change.

Now let us go back and perform the experiment as it should be without the extra assumption. That means each pair is polarised in the same plane.

1. First you perform the experiment exactly as described (same distance analysers) for a certain duration.
The result should be that counter 1 and 2 (+ direction) should be close to 50% of the total number of events.
The result for Counter 3 and 4 (- direction) should be the same and also 50%
It is very important to compare the results of C1 and C2 with the Coincidence Monitor and observe that they are simultaneous. The same with C3 and C4. Comparing C1 with C3 than ofcourse they are not simultaneous.
2. You repeat the same experiment but you change the angle of filter 1 to 90 degrees.
The results are identical as before: each counter get incremented in 50% of all events.
It is very important if you compare the results of C1 and C2 with the Coincidence Monitorto observe that they are not simultaneous. The same with C3 and C4. In this case c3 is simultaneous with C2 and C1 with C4.
3. Next you repeat the same experiment (both filters 0 degrees) but you insert a second analyser in the left beam between the first and the source
The idea behind this change is to make the experiment asymetrical and "to measure" the left stream first.
The result should be that counter 1 and 2 (+ direction) should be close to 50% of the total number of events.
The fact that there are two filters in the left beam should have no influence on counter 1
The result for Counter 5 and 4 (- direction) should be the same and also 50%
Counter 3 should be zero

With the CM you should also see no difference. C1 and C2 are simultaneous and C5 and C4 are simultaneous.
```                                  Experiment

0 degrees  0 degrees                 X      0 degrees
Counter 1<---Filter1<---Filter3<----Source--------------->Filter2--->Counter 2
^ (+)        |         |                      X          |          ^ (+)
|            V         V                                 V          |
|        Counter 3  Counter 5                        Counter 4      |
|            ^ (-)     ^  (-)                            ^ (-)      |
|            |         |                                 |          |
-------------------------Coincidence Monitor-----------------------
```
4. You repeat the same experiment, (asymetrical setup) but during the experiment you change the angle of analyser 3 to 90 degrees and backward to zero.
5. This should have no effects on the total number of counts for C5, C4 and C2. They should be equal to 50%.
However there should be an effect on C1 and C3. During the period that analyser 3 is 90 degrees C1 should not increase, instead C3 should increase. The total number of counts of C1 and C3 should stay constant and be 50%.
6. Changing the angle of analyse 3 should als have an effect if you monitor C4 and C5 with the CM . When the angle of Filter3 is zero then they are simultaneous. When the angle is 90 degrees they are not. This is the case when No teleportation is involved.
7. You will not see any difference with the CM when you compare C4 with C5 when teleportation is involved.
Teleportation comes from the fact that the two photons are physical connected even at large distances. This implies if you change one the other one should also change.
The left one is changed near analyser 3, half way between Filter 1 and the source, that means the right one should also change half way between Filter 2 and the source and that is at the locations identified with the two "X X".

### Answer Question 6: Teleportation in slow motion.

In order to demonstrate Teleportation in Slow motion we use Domino Pieces.
The following sketch shows the layout of the pieces
```     Teleportation with domino pieces.
Finish 1                                  Finish 2
1 1 1 1 1 1 1 1 1 1  S  2 2 2 2 2 2 2 2 2 2
O1                  1   2                  O2
1 2
3
^    3
|    3
|    3
|  start
```
The setup of the dominos pieces is the following:
1. There is a vertical path, identified with with the number 3. There is also the starting point.
2. Next we have a switch point or branch point where vertical path is divided into two branches.
3. One branch goes to the left, identified with the number 1. At the end is the finish and an Oberver (O1)
4. The other branch goes to the right, identified with the number 2. At the end is the finish and an Oberver (O2)

The demonstration is very easy.

• First we demonstrate that this experiments works. We push the first piece at the start. It falls. Then the next etc. We see the branch. Now the left pieces start to fall and simultaneous the right pieces. Until the last pieces, at each end, reach the finish and fall. Then it is all over.
• We can repeat this experiment. First we do a setup and the we push once and we observe until the two final pieces fall.
• Now we perform the experiment again but this time slightly different. The Observer at the left finish (O1) holds with his hand the last piece fast, such that it cannot fall.
• You start the experiment as before. The beginning is the same as before but there is a difference in the left branch. When the falling pieces reach the left finish, the final piece will not fall.
Now there are two possibilities:
1. The last piece at the right side will fall.
2. The last piece will not fall
The last case is called: Teleportation. Observe that this is a symetric behaviour.

I expect that the reaction of the reader is: you will not see teleportation. I agree.
However this experiment is not so strange as it seems. Compare it with the experiments in the documents 4 and 5 in the Literature. In those documents

• two entangled photons are used to replace the domino pieces.
• two beam splitters are used in what is called the finish in the domino experiment.
• a third photon is used as the message transported compared with hold the last left piece fast with your fingers.
One of the biggest problems is how do you take care that the two moments, one that message (i.e. the third photon) and two that the entangled photon reaches the left beam splitter (the sender), are simultaneous? IMO this is very difficult.
That is also the same moment that the other photon pair reaches the right beam splitter (the receiver)

One other problem what is the behaviour at the receiver beam splitter in the two cases: (a) no teleportation versus (b) teleportation. Neither document discusses that nor explains it.

### Answer question 7: What means "Spooky action at a distance"

"Spooky action at a distance" is related to Teleportation. In the above paragraph you can read that if you change the state of photon A of a photon pair than photon B should also change, even if A and B are miles apart
This effect is nicknamed "Spooky action at a distance" and takes place instantaneous. In effect much faster than the speed of light.
As such it is in conflict with Special Relativity.

### Answer question 8: What means Locality versus Non Locality

Local means that the cause of any change is something that happened in the neighbourhood of that change. This change is propagated through space. The maximum speed is the speed of light.
The concept of neighbourhood is flexible. In fact the further away (the larger the neighbourhood) the longer ago something happened.

Non Locality means that the cause of change is non local but happened at far distance. In fact non-locality implies that a change here can have an instantaneous impact in a change overthere at far distance.
The speed of propagation involved is much larger than the speed of light. As such is in conflict with Special Relativity.

Albert Einstein was a proponent of the Local concept. Niels Bohr a proponent of Non Locality

### Literature about teleportation of photons

1. Experimental demonstration of five-photon entanglement and open-destination teleportation Article in Nature
2. Teleportation goes long distance
3. Teleportation using squeezed single photons
4. Physics News Graphics - Quantum Teleportation With three photons. Simple Graphic
5. Quantum Teleportation With three photons. More complex Graphic.
6. Quantum Teleportation, Information and Cryptography Same subject as #4 and #5. Discussion is more technical.
We time it so that both E1 and K reach the beam splitter at the same time.
How do you do that ?

### Reflection part 1

IMO none of the two experiments will actual demonstrate teleportation i.e. will demonstrate that, if you make a change at the end of left beam, without any change at the source, that the behaviour at the end of the right beam will also change
What is important to remark that both experiments are asymetrical while if they demonstrate teleportation that the results are symetrical.
The experiment with the domino pieces has that same characteristic.

### Reflection part 2

The following is an interesting document: Einstein's Spooks and Bell's Theorem This document explains both the outcome of an EPR experiment using the Bell's theorem (the Bell inequalities) and Quantum Mechanics
The EPR experiments demonstrate very significant violations of the Bell Inequalities while confirming the predictions of quantum mechanics.
There are no details how the actual EPR experiment was performed.
and:
Locality was in conflict with experiment
This means that Einstein, Podolsky and Rosen are Wrong.
The question is: is that conclusion correct.
IMO the only thing what the experiments demonstrate is that two photons are correlated i.e. are entangled.
The most logical explanation is that this correlation is established at the source. The experiments do not show the opposite.
The fact that this correlation is non lineair does not prove that Einstein is wrong. IMO it also would not have changed his opinion.

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Created: 29 May 2009