Photon entanglement: why three angles?

[atyy]

They do talk about it, but they don't explain it. Try to answer the question in your own words, with a sentence or two, and maybe you'll see the same paradox I see. Or maybe you'll see an explanation, that's even better.

They do. Read the papers.

 

[johana]

Isn't it when the photon is detected by an apparatus, it is then that the system takes on the polarisation of the polariser?

It is when the first photon A interacts with the polarizer A that its "wave function collapses", which we are meant to understand its, until then, "undefined" polarization becomes real and defined by the polarizer A. At the same time, or a bit later, the other photon B, whose polarization was also undefined until then, acquires the same definite polarization as the first photon A. From there on both photons are in "classic" mode of operation, having definite polarization, and so the interaction between second photon B and polarizer B goes on normally in accordance to Malus law.

 

[stevendaryl]

Yes, loophole. But what loophole are you talking about? FTL loophole is addressed by separating polarizers far enough apart relative to the time interval between when signal and idler photon are supposed to meet with their polarizers. It works for any individual angle when tested separately, so that's not it.

No, that is it. If angles a and b are chosen too far in advance, then you can't be certain that the hidden variable isn't influenced by those settings.

 

[stevendaryl]

They do talk about it, but they don't explain it. Try to answer the question in your own words, with a sentence or two, and maybe you'll see the same paradox I see. Or maybe you'll see an explanation, that's even better.

No, I don't know what paradox you are talking about.

 

[stevendaryl]

It is when the first photon A interacts with the polarizer A that its "wave function collapses", which we are meant to understand its, until then, "undefined" polarization becomes real and defined by the polarizer A. At the same time, or a bit later, the other photon B, whose polarization was also undefined until then, acquires the same definite polarization as the first photon A. From there on both photons are in "classic" mode of operation, having definite polarization, and so the interaction between second photon B and polarizer B goes on normally in accordance to Malus law.

That's the "collapse" interpretation of EPR, but it's explicitly nonlocal.

 

[Nugatory]

It is accepted by both sides time2 is less than time3, otherwise causality would be acting backwards in time, and that's not really kind of thing local realists are hoping for. Each subsequent time is greater or equal to previous time:

Time1 is not necessarily less than time3. You can set up the experiment in such a way that some of the people watching the experiment observe that photon A reaches polarizer A before photon B reaches polarizer B while others (who happen to be moving relative to the first group) observe that photon B reaches polarizer B before photon A reaches polarizer A. This is Einstein's "relativity of simultaneity" (google for that phrase if you're not already familiar with it) at work.

Because we cannot directly observe photon B acquiring 0° polarization, we don't know if time2 is different from time3 (it's natural to expect that it is, but that expectation comes from our day-to-day experience, which is a poor guide to how QM works). However, if time2 is different from time3, it will always be less than time3 for all observers.

Please note those time events marked with arrows, are they anyhow relevant to what happens at time1, time2, or time3?

As long as they are all greater than time0 the changes to the A setting cannot affect the result at B (and vice versa) in any local theory. Yet the quantum mechanical result is that the result at B depends on the setting at A at time0.9 - the reason for doing the fast switching experiments is to confirm that this is indeed the case.

 

[RUTA]

time0: photons A & B emitted with unknown/undefined polarization

time1: photon A goes through 0° polarizer A and acquires 0° polarization

time2: photon B acquires 0° polarization, for some reason ( time1 = time2 ?? )

time3: photon B with 0° polarization interacts with 0° polarizer B, so it too goes through


Now, if polarizer B was at 90° and switched to 0° just a moment before time3, what difference does it make?

Let's look at the Hardy state from the Mermin paper in my post #21. You have two particles, two settings 1 and 2, two outcomes R and G. Here are the facts for that state being measured in this configuration taken from p 881:

The data exhibit the following important features:

(a) In runs in which the detectors end up with different
settings, they never both flash green: 21 GG and
12 GG never occur.

(b) In runs in which both detectors end up set to 2, one
occasionally finds both flashing green: 22GG sometimes
occurs.

(c) In runs in which both detectors end up set to 1, they
never both flash red: 11RR never occurs.

Now suppose you're particle 1 and know ahead of time that you both will be measured in setting 2. You agree with your partner that you'll both give a G result, i.e., 22GG. As you approach your detector you see that it's set to 1. What do you do?

Suppose you choose to be 1R, thinking your partner will be 2G and you have to satisfy condition (a). But, what happens if your partner also encounters setting 1 and, thinking the same thing, decides to be 1R. Now you have a 11RR outcome in violation of (c). Suppose you go with 1G. Now if your partner's detector isn't changed and he thinks all is ok and goes with 2G you have a 12GG outcome in violation of (a). So, by encountering a setting that isn't what you expected you're screwed.

Is that clear enough?

 

[stevendaryl]

Let's look at the Hardy state from the Mermin paper in my post #21. You have two particles, two settings 1 and 2, two outcomes R and G.

Yes. In my opinion, even though Bell's inequality might be more amenable to experimental tests, when it comes to discussions about the weirdness of quantum mechanics and entanglement, the Hardy state is much easier to understand. The impossibility of a local, deterministic hidden-variables explanation is much clearer, since you don't really need to do any kind of mathematics involving expectation values, or probability calculations, or whatever. You have a situation which clearly is impossible, classically, yet happens, quantum mechanically.

 

[Johan0001]

Suppose you choose to be 1R, thinking your partner will be 2G and you have to satisfy condition (a). But, what happens if your partner also encounters setting 1 and, thinking the same thing, decides to be 1R. Now you have a 11RR outcome in violation of (c). Suppose you go with 1G. Now if your partner's detector isn't changed and he thinks all is ok and goes with 2G you have a 12GG outcome in violation of (a). So, by encountering a setting that isn't what you expected you're screwed.

Is that clear enough?

This is the big mystery.
Could you give a reference to which experiment best exploits this phenomena, with the least possible loopholes such as reality and locality?

 

[DrChinese]

This is the big mystery.
Could you give a reference to which experiment best exploits this phenomena, with the least possible loopholes such as reality and locality?

Some of the most important include these:

http://arxiv.org/abs/quant-ph/9810080
Violation of Bell's inequality under strict Einstein locality conditions
Gregor Weihs, Thomas Jennewein, Christoph Simon, Harald Weinfurter, Anton Zeilinger (University of Innsbruck, Austria)
(Submitted on 26 Oct 1998)

We observe strong violation of Bell's inequality in an Einstein, Podolsky and Rosen type experiment with independent observers. Our experiment definitely implements the ideas behind the well known work by Aspect et al. We for the first time fully enforce the condition of locality, a central assumption in the derivation of Bell's theorem. The necessary space-like separation of the observations is achieved by sufficient physical distance between the measurement stations, by ultra-fast and random setting of the analyzers, and by completely independent data registration.

http://www.nature.com/nature/journal/v409/n6822/full/409791a0.html
Experimental violation of a Bell's inequality with efficient detection

M. A. Rowe1, D. Kielpinski1, V. Meyer1, C. A. Sackett1, W. M. Itano1, C. Monroe2 & D. J. Wineland1


http://arxiv.org/abs/1306.5772
Detection-Loophole-Free Test of Quantum Nonlocality, and Applications
B. G. Christensen, K. T. McCusker, J. Altepeter, B. Calkins, T. Gerrits, A. Lita, A. Miller, L. K. Shalm, Y. Zhang, S. W. Nam, N. Brunner, C. C. W. Lim, N. Gisin, P. G. Kwiat
(Submitted on 24 Jun 2013 (v1), last revised 26 Sep 2013 (this version, v2))

We present a source of entangled photons that violates a Bell inequality free of the "fair-sampling" assumption, by over 7 standard deviations. This violation is the first experiment with photons to close the detection loophole, and we demonstrate enough "efficiency" overhead to eventually perform a fully loophole-free test of local realism. The entanglement quality is verified by maximally violating additional Bell tests, testing the upper limit of quantum correlations. Finally, we use the source to generate secure private quantum random numbers at rates over 4 orders of magnitude beyond previous experiments.

 

[johana]

Here's something from DrChinese younger self.

https://www.physicsforums.com/showthread.php?t=39614&page=7

Despite what you (and others) might think, you don't need to change polarizer settings in flight or otherwise vary the angles to test Bell's Theorem. You only need to calculate the correlation percentages at three particular angle settings (these can be done fully independently). Then combine a la Bell.

Varying is only necessary if you are asserting that the measurement devices are (or might be) communicating with each other so as to affect the outcome of the correlation tests. We already know from Aspect that doesn't happen, because he did the experiments both ways and there was no difference in the outcomes! Even that should be a definitive conclusion of Aspect. Further regarding the varying issue:

a. If you are a local realist, I would assume that wouldn't be much of an issue to you since you think there are classical, intuitive explanations for everything anyway - strange new types of communication between measuring devices should not be an issue.
b. If, on the other hand, you follow the Copenhagen interpretation, varying also shouldn't matter as you don't isolate out communication with other parts of the measurement apparatus for any other type of experiment (such as double slit) either.
c. Also, if you believe the correlation is non-local then the varying analyzers are superfluous.
d. And finally, if you are a local non-realist like me :) then you already believe that the only "real" component being measured is the angle between the remote polarizers anyway i.e. the measurement is fundamental to the process.

This makes perfect sense. Switching angles is unnecessary and is not a substitute for placing detectors far apart. It's about some out of this world type of theory neither nonlocalists nor local realists care to imagine even in their wildest dreams. The only thing that doesn't make sense is "local non-realist". What in the world is that?

 

[stevendaryl]

This makes perfect sense. Switching angles is unnecessary and is not a substitute for placing detectors far apart. It's about some out of this world type of theory neither nonlocalists nor local realists care to imagine even in their wildest dreams. The only thing that doesn't make sense is "local non-realist". What in the world is that?

The quote from Dr. Chinese points out that switching angles in-flight is only unnecessary because people have ALREADY showed that it makes no difference. To demonstrate that there is no local, classical explanation for EPR, you have to check out the possibility that the filter settings affect the outcome in a slower-than-light way.

 

[johana]

The quote from Dr. Chinese points out that switching angles in-flight is only unnecessary because people have ALREADY showed that it makes no difference. To demonstrate that there is no local, classical explanation for EPR, you have to check out the possibility that the filter settings affect the outcome in a slower-than-light way.

Switching angles does not relate to any local or classical explanation, it's about nonlocal correlation between polarizers, not just photons. No one is proposing that, they are just messing up measurements with additional unnecessary complexity and randomness.


DrChinese explains redundancy of it well here:

a. If you are a local realist, I would assume that wouldn't be much of an issue to you since you think there are classical, intuitive explanations for everything anyway - strange new types of communication between measuring devices should not be an issue.

b. If, on the other hand, you follow the Copenhagen interpretation, varying also shouldn't matter as you don't isolate out communication with other parts of the measurement apparatus for any other type of experiment (such as double slit) either.

c. Also, if you believe the correlation is non-local then the varying analyzers are superfluous.

d. And finally, if you are a local non-realist like me :) then you already believe that the only "real" component being measured is the angle between the remote polarizers anyway i.e. the measurement is fundamental to the process.

 

[DrChinese]

The only thing that doesn't make sense is "local non-realist". What in the world is that?

There are a number of non-realistic interpretations. Not everyone will concur with my categorization, but this is an answer to your question.

We all know that the Bohmian group (de Broglie-Bohm, Bohmian Mechanics) and several others are explicitly non-local. So I call anything that is not EXPLICITLY non-local to be "non-realistic" by definition (to comply with Bell). That would then include: Many Worlds, Relational Blockworld (ask RUTA about that), Cramer's Absorber, Aharanov's Time Symmetric QM, and a few others.

You mentioned something in an earlier post about non-causal situations (future affects the past). Before you rule those out, you might take note: there are substantial experiments that demonstrate the future affects the past. These experiments are not a rock solid proof of same, but they are definitely powerful evidence. For example:

http://arxiv.org/abs/quant-ph/0201134
Experimental Nonlocality Proof of Quantum Teleportation and Entanglement Swapping
Thomas Jennewein, Gregor Weihs, Jian-Wei Pan, Anton Zeilinger
(Submitted on 29 Jan 2002)

"Quantum teleportation strikingly underlines the peculiar features of the quantum world. We present an experimental proof of its quantum nature, teleporting an entangled photon with such high quality that the nonlocal quantum correlations with its original partner photon are preserved. This procedure is also known as entanglement swapping. The nonlocality is confirmed by observing a violation of Bell's inequality by 4.5 standard deviations. Thus, by demonstrating quantum nonlocality for photons that never interacted our results directly confirm the quantum nature of teleportation. "

See page 5. All of this is garden QM, as time ordering is not critical in many setups using entangled systems.

 

[stevendaryl]

Switching angles does not relate to any local or classical explanation, it's about nonlocal correlation between polarizers, not just photons.

I'm not sure what is the root of our communication problems, but something is not getting communicated here. Switching angles at the last possible minute does relate to local or classical explanations in the sense that it proves that there are no such explanations. If you DON'T switch, then that leads to the possibility that the settings affect the hidden variable in a local way.

No one is proposing that, they are just messing up measurements with additional unnecessary complexity and randomness.

They're closing a possible loophole. That's all. I don't understand what it is that you don't understand about it.

 

[johana]

Switching angles at the last possible minute does relate to local or classical explanations in the sense that it proves that there are no such explanations. If you DON'T switch, then that leads to the possibility that the settings affect the hidden variable in a local way.

Varying is only necessary if you are asserting that the measurement devices are (or might be) communicating with each other so as to affect the outcome of the correlation tests.

Do you disagree with this? Are you suggesting supposed communication between distant measurement devices is a local theory?

 

[DrChinese]

Do you disagree with this? Are you suggesting supposed communication between distant measurement devices is a local theory?

When you say "distant measurement devices" in this context, we all know that means devices that are sufficiently far apart so that no signal could move from one to the other at a speed less than c so that Alice's setting could be transmitted to Bob (and vice versa). A typical batch of observations takes a few minutes. So that only helps if Alice and Bob are FAR removed from each other because after 1/20 of a second, there is no place on Earth that far removed. So you must randomly select and change settings very fast: fast switching.

To put things in context: a nanosecond is about a foot. Bell tests are usually done perhaps 5 to 500 feet apart (although much larger distances have been done too). And PDC pair production is on the magnitude of 1,000-10,000 per second.

The idea of fast switching was to PROVE there could be no communication between distant measuring devices via some sub-c mechanism which did not fit into any theory at all. If you can imagine, the local realist was trying to say: "There COULD be something local occurring that QM does not contemplate." Fast switching proves that wrong.

 

[johana]

We all know that the Bohmian group (de Broglie-Bohm, Bohmian Mechanics) and several others are explicitly non-local. So I call anything that is not EXPLICITLY non-local to be "non-realistic" by definition (to comply with Bell). That would then include: Many Worlds, Relational Blockworld (ask RUTA about that), Cramer's Absorber, Aharanov's Time Symmetric QM, and a few others.

I'm not sure "non-realistic" is adequate substitute for "non-local". How about Newton's gravity, would you say it's non-local just because interactions are instantaneous?

 

[DrChinese]

I'm not sure "non-realistic" is adequate substitute for "non-local". How about Newton's gravity, would you say it's non-local just because interactions are instantaneous?

"Non-realistic" is not a substitute for "non-local" in any sense I am aware.

Traditional Newtonian gravity is non-local, yes definitely.

 

[johana]

The idea of fast switching was to PROVE there could be no communication between distant measuring devices via some sub-c mechanism which did not fit into any theory at all. If you can imagine, the local realist was trying to say: "There COULD be something local occurring that QM does not contemplate." Fast switching proves that wrong.

The problem is that it's usually described as an essential part of the experiment, which makes it far from obvious it's just there to close some loophole no one even cares about.

Traditional Newtonian gravity is non-local, yes definitely.

Classical electromagnetism too. So the whole of classical physics was already non-local even before there was any QM. Why are we surprised then? What is different between QM non-locality and classical physics non-locality?

 

[stevendaryl]

Classical electromagnetism too. So the whole of classical physics was already non-local even before there was any QM. Why are we surprised then? What is different between QM non-locality and classical physics non-locality?

I wouldn't say that classical electromagnetism was nonlocal. Classical electromagnetism is the paradigm example of a local theory---no effect can propagate faster than the speed of light.

 

[johana]

I wouldn't say that classical electromagnetism was nonlocal. Classical electromagnetism is the paradigm example of a local theory---no effect can propagate faster than the speed of light.

I wouldn't call it non-local myself, but Coulomb and Lorentz force equations assume instantaneous interaction over distance just like Newton's law of gravity. Whether instantaneous action over distance indeed implies "non-local", I'm not sure, that's the question.

 

[billschnieder]

Fast random switching has nothing to do with non-locality. It is done *only* to eliminate the possibility that Alice and Bob have conspired in advance to manipulate the results. As to the topic question, "Why 3 angles". Actually almost no experiments measure 3 angles. They measure 4. And that is because nobody uses the original Bell's inequalities, they all use the CHSH version which is based on 4 angles. So the reason why they use 3 angles rather than just 2 is because they are not primarily trying to test the QM prediction, but also to test the inequality which was derived using 3 angles (Bell) or 4 angles (CHSH).

BTW: I do not share the believe that those inequalities actually apply to the experiments they are being used for, as has been discussed many times here already, and in the literature.

 

[Avodyne]

Coulomb and Lorentz force equations assume instantaneous interaction over distance just like Newton's law of gravity. Whether instantaneous action over distance indeed implies "non-local", I'm not sure, that's the question.

The complete EM interaction is not instantaneous. If two stationary charges are one light-year apart, and then you move one of them, the total force felt by the other charge does not change until one year later. The same is true of the gravitational force in general relativity.

What is different between QM non-locality and classical physics non-locality?

See this article by David Mermin from 1985: https://cp3.irmp.ucl.ac.be/~maltoni/PHY1222/mermin_moon.pdf
Begin with "A gedanken demonstration" on page 4.

 

[DrChinese]

What is different between QM non-locality and classical physics non-locality?

As a matter of convention, "classical physics" usually considers General Relativity rather than Newtonian gravity, making c fundamental. Further, causes precede effects and the observer does NOT have a fundamental role in defining reality ("the moon is there when no one looks").

We now realize that this neat and pretty picture of our universe is not accurate. Of course, beauty is in the eye of the beholder.

 

[johana]

Fast random switching has nothing to do with non-locality. It is done *only* to eliminate the possibility that Alice and Bob have conspired in advance to manipulate the results.

Is it about determinism, choice and free will? Is it actually a part of the inequality derivation?

BTW: I do not share the believe that those inequalities actually apply to the experiments they are being used for, as has been discussed many times here already, and in the literature.

There you said this:

In other words, as Alice or Bob rotates their polarizers, the coincidence counts change.

Is that coincidence count the same thing as the number of matching pairs? Isn't it supposed to change as Alice or Bob rotate their polarizers, what's your objection about?

 

[DrChinese]

Is that coincidence count the same thing as the number of matching pairs? Isn't it supposed to change as Alice or Bob rotate their polarizers, what's your objection about?

You are asking billschnieder's viewpoint. As he and I have had many discussions about this point, I will pass this on - and which you should take as a fair summary:

1. billschnieder is a local realist. Post-Bell, local realism is generally not considered viable.

2. Discussing the pro's and con's of local realism is outside of the scope of this thread. If you want to discuss his viewpoint and reasoning further, that should be in a new thread.

3. Even in a new thread, you should be aware that this is a moderated forum in which generally accepted science is discussed. No one has the right to put forth their own personal opinions when such viewpoint does not have suitable references to support same. You can check the forum guidelines for details, but that policy is enforced.

 

[billschnieder]

Is it about determinism, choice and free will? Is it actually a part of the inequality derivation?

Neither. It is only for avoiding a conspiracy in which Alice and Bob freely chose in advance to manipulate the results and fool everyone else.

Is that coincidence count the same thing as the number of matching pairs? Isn't it supposed to change as Alice or Bob rotate their polarizers, what's your objection about?

Yes, coincidence count means the same as number of matching pairs. Trick question: is coincidence a local result, Why can't you use coincidence to send information?

As to the other question, you can find my answer here.

 

[johana]

Neither. It is only for avoiding a conspiracy in which Alice and Bob freely chose in advance to manipulate the results and fool everyone else.

Why are there three angles in the derivation then?

Yes, coincidence count means the same as number of matching pairs. Trick question: is coincidence a local result, Why can't you use coincidence to send information?

Because each side receives only half of the whole information?

 

[stevendaryl]

Why are there three angles in the derivation then?

Because three works and two doesn't.