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More than 50 years ago, John Bell proved that no theory of nature that obeys Locality and Realism can produce all the predictions of quantum theory; in any local-realist theory, the correlations between outcomes of measurements on distant particles satisfy an inequality that can be violated if the particles are entangled.
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This introduction is different than the "News and View" article about the same subject. The emphasis is on entanglement and gives an impression that entanglement is an important parameter if you want to demonstrate faster than lightsignals.
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Here we report a Bell experiment etc.
We use an event-ready scheme that enables the generation of robust entanglement between distant electron spins.
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Also here the emphasis is on entanglement.
If you want to do that you need to explain by means of a separate experiment how this entanglement is measured.
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In particular, if the input bits can be considered free random variables etc then the following inequality holds under local realism:
- S = |(0,0)+(0,1)+(1,0)-(1,1)|<= 2 (equation 1)
where (a,b) denotes the expectation value of the product of x and y for input bits a and b.
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When you test equation 1 with the 4 expectation values: 0.5, 0.5, 0.5 and -0.5 the result S = 2
What you also see is that the equation is not symeteric. This raises the question why this particular notation?
Why not write this equation as:
- S = |(0,0)|+|(0,1)|+|(1,0)|+|(1,1)|<= 2 (equation 1a)
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The issue is, what is the result when I perform one measurement.
How many expectation values can be one?
What would be interesting are the results in tabular form off all the measurements (245 trials) of one complete experiment.
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For each trial the two spins of each electron are prepared into the entangled state:
- psi = (|^V> - |V^>)sqr(2)
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It is interesting to know why this particular state.
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The spin in box A is then measured along direction Z or direction X
and the spin in box B is measured along (-Z+X)sqr(2) or (-Z-X)sqr(2)
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It is important to know why these two particular directions.
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IF the measurement outcomes are as output of the boxes, then quantum theory predicts a value of S = 2sqr(2), which shows the combination of locality and realism is fundamentally incompatible which the predictions of quantum mechanics
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which claims that S = 2.
In this sentence both the words quantum theory and quantum mechanics are used. The difference if any should be explained.
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Bell's inequality provides a powerfull recipe for probing fundamental properties of nature; all local-realist theories that specify where and when the free random input bits and output values are generated can be experimentally tested against it.
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Sorry to say but this sentence is rather obscure, vaque.
The left side of the CHSH-Bell inequality specifies a mathematical relation based on two variables, which can be calculated for an experiment.
The issue is the physical interpretation for values smaller and larger than 2.
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Violating Bell's inequality with entangled particles poses two main chalenges: excluding any possible communication between the boxes (1) Locality Loophole and guaranteeing efficient measurements (2) Detection Loophole .
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When you perform any experiment the whole setup should be clear and ambiguous.
When you perform an experiment with a dice the logical outcome that the chance of throwing any number should be the same. If that is not the case the issue should not be any form of cheating.
In that same sense comunication between the boxes (1), if not explicitly described, is interpreted as sabotage.
efficient measurements (2) in the realm of quantum mechanics is a dream if accuracy is involved.
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First, if communication is possible, a box can in principle respond using knowledge of input settings, rendering the Bell inequality invalid.
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If you ask someone to answer a sequence of questions, but at the same time you also give him the answers you are cheating. The description of the experiment should be complete.
The whole concept of entangled particles is a physical issue and depents abouts the process or reaction that generates these particles.
IMO there are many processes which creates two or more photons. IMO in most of the processes the "direction" or "orientation" of these photons is completely random. If they are not than a simple mathematical operation can distinquish between the two.
0.75
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0 ---------------------------
0,0 1.0 0.1 1.1
Figure 1 A - Random
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0 -----------------------
0,0 1.0 0.1 1.1
Figure 1 B - parallel
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0,0 1.0 0.1 1.1
Figure 1 C - anti parallel
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Figure 1 shows 3 specific results where two particles (photons) are involved.
In each case the orientation of the particle is measured by means of a beam splitter in opposite directions. The orientation is the same, that means both measure in the +x or -x direction.
- Figure 1 A represents a random result.
That means first that there is a 50% chance that the result in one direction is +x and secondly in that situation, that there is a 50% chance that the other one is also +x. That means the overall chance is 25%.
This is also true for all the other 3 combinations.
- Figure 1 B represents the parallel situation.
That means first that there is a 50% chance that the result in one direction is +x and secondly when that is the case the other one is also +x. That means the overall chance is 50%
The same is true in the -x direction. The overall chance for the -x,-x combination is 50%.
The chance for the other two combinations (+x,-x) and (-x,+x) is practically zero.
- Figure 1 C represents the anti parallel situation.
That means first that there is a 50% chance that the result in one direction is +x and secondly when that is the case the other one is always -x. That means the overall chance is 50%
The same is true in the -x direction. The overall chance for the -x,+x combination is also 50%.
The chance for the other two combinations (+x,+x) and (-x,-x) is practically zero.
This is the situation which we call: entanglement
The explanation is in the process that creates the two particles or photons.
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A C B
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| M . . M |
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|RNG / \ RNG|
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s-p s-p
Res Res
-0.7 0.0 0.7
Figure 2 Space-time analysis of the experiment.
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Figure 2 is a simplification.
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After spin initialization (res), spin-photon (s-p) entanglement is generated such that the two photons from A and B arrive simultaneous at C where the detection time is recorded.
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M is the measurement symbol
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0.65 ....... .......
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0.5 . . . . .......
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(a,b) (0,0) (0,1) (1,0) .(1,1).
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-0.5 .......
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Figure 4 Loophole-free Bell inequality violation.
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Summary of the data and the CSH correlations
The read-out bases corresponding to the input values are indicated by the green and blue arrow.
Dotted lineslines indicate the expected correlation on the basis of the spin read-out fidelities and the characterization measurements presented in Fig 3
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Figure 4 above only shows the dotted lines
When you want to calculate S using equation 1 you get: 0.65+0.65+0.5-(-0.5)=2.3
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(3)Our experiment realizes the first Bell test that simulataneously addresses both the detection loophole and the locality loophole. Being free of experimental loopholes, the set-up tests local-realist theories of nature without introducing extra assumptions such as fair sampling, a limit on (sub-) luminal communication or the absence of memory in the set-up.
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See: Reflection 3 - Loopholes
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In fact, our experiment already enables tests of all models that predict that the random input bits are determined a maximum of 690 ns before we record them.
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If you start from entangled electrons the first part should be a separate experiment to demonstrate that the electrons are entangled.
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Reflection 1
The central part of this document is the experiment depicted in Figure 1. The question is what does it demonstrate.
The idea behind the experiment in some sense is to demonstrate that faster than light communication is possible, however the text does not clearly stipulate that. In the text we discuss "Locality".
The central part of the whole experiment is equation 1. Equation 1 is a calculation of a parameter S, which value can not be larger than 2.
The outcome of the experiment is that S=2.42, which is in disagreement which equation 1. What does that mean?
If you want to understand equation 1 better, you have to perform the same experiment under more different conditions.
The strategy is to perform the experiment as simple as possible. Forget the loopholes as if someone trying to sabotage your experiment.
- One device that should be removed is the RNG or random number generator. My understanding is that RNG generates 4 conditions. That means the experiment should be performed for each condition separately.
- A second thing what you should also not do is to perform a measurement on the spin of the electrons.
Reflection 2 - Measurement
What is a Measurement?
A measurement is a human action in order to quantify a physical parameter of a process.
Suppose I want to know the water temperature of my pool. To do that I need a thermometer.
I put the thermometer in the water. I take it out and I read the result. The result is one measurement of exactly 10.000 degrees.
Does that mean that the water of my pool is 10.000 degrees. To know that answer, you have to perform 1000 experiments at all different locations in the pool. The result is an average value and additional statistical parameters as a result of all the measurements.
However this are only the statistical results for one day. To make this more general you have to perform this same experiment many more times.
What is the importance of this discussion. The importance is one day if you only perform this experiment once and you read the temperature of the water and someone asks you questions about the temperature of the pool you can answer him or her about the total condition of the pool based on this only one measurement. If someone else at the opposite site of the pool is also performing one measurement you can already predict what his reading will be without any communication. In fact your measurement does not influence his measurement.
The same issue exist with entanglement.
In Figure 1A, 1B and 1C the result of the measurement of three different processes is discussed. Only in Figure 1 C the result is described as entanglement. In the process two particles are created (at regular intervals) and when that is the case and both particles are measured only the combinations (+x,-x) and (-x,+x) are detected.
That means
- that when only one is measured you know the other combination
- that when neither is measured you know that the orientation is anti parallel.
The act of measuring has no influence on this. Nor is any faster than lightsignal communication involved. Your knowledge is simply the result of 1000 identical experiments.
However everything is slightly more complication. When you perform a measurement with a beamsplitter and the particle can either left or right, what you measure is the state (orientation) of the particle before the beamsplitter. The beamsplitter can influence the orientatation, implying that you cannot measure the state twice. Or if you do it is not guaranteed that you will measure the same orintation twice
Reflection 3 - Loopholes
One important concept of the experiment is that there are no loopholes.
For any experiment there consist a golden rule that it should be repeated by other independent organizations. If that is not possible or errors are discovered the claims of the original experiment are invalid.
What is a Locality Loophole ? See (1) and (3)
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Created: 30 March 2014
For further reading: The Quantum Theory and Reality Critical evaluation of the Scientific American Article by Bernard d'Espagnat.
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