Uncertainty and entanglement relationship

[wmikewells]

Is there a hard and fast relationship between uncertainty and entanglement? In other words, if you have one phenomena, you have to have the other. I would think so because of the following example, but I wanted to make sure I understood the relationship. Please let me know if there are better examples or if there is no relationship. There is probably something wrong with my example anyways.

Example: Let's say there are two horizontal electron guns facing each other that fire a single electron each at the same time. The electron from the left gun is called the L electron, and the electron from the right gun is called the R electron. The left gun has a filter on it that blocks all but spin up electrons, and the right gun has a filter to blocks all but spin down electrons. In addition, let's say that there are two electron spin detectors: one above (detector A) and below (detector B) the impending collision. Assuming that the electrons collide and that the detectors will record the electrons spin, there will always be two interpretations of the collision before the spin (and what happened) is determined.

Interpretation 1: Electron L went to detector A and electron R went to detector B
Interpretation 2: Electron L went to detector B and electron R went to detector A

Both are equally probable and there is no certain way to determine which happened until the spins are detected. Because of this uncertainty, the two electrons must be entangled. Otherwise, weird cases would result such as electron R being detected in both detectors and electron L disappearing. Or, one observer seeing one thing and another observer seeing another.

 

[DrChinese]

I am not sure your example is appropriate, but I am sure your use of terminology could use some sharpening. Entangled particles are more often called "indistinguishable" rather than "uncertain". *All* quantum particles/systems, including those which are entangled, obey what is called "the uncertainty principle".

If 2 electrons are scattered in such a way that they are indistinguishable, they will be entangled. I would not say that would be the expected result of most such interactions.

 

[wmikewells]

Thank you for the clarification. That helps. I guess I am asking if there is a theoretical relationship (A therefore B) between the uncertainty principle and entanglement (or non-locality) versus just an observational one (A & B) and whether there is a simple example to make sense of it.

I did some more research after I posted, and I found an article that shows a theoretical relationship between the two (not that I understand it entirely). Surprise Link Between Weird Quantum Phenomena: Heisenberg Uncertainty Principle Sets Limits On Einstein's 'Spooky Action at a Distance'. Nov. 19, 2010. See link below.

http://www.sciencedaily.com/releases/2010/11/101118141541.htm

If there is a theoretical relationship between the two, I would expect that some sort of experiment (thought or real) would be possible to show that relationship. My example probably falls well short of demonstrating that relationship. It was a stab in the dark. I was trying to show that the quantum system "must" be entangled because the state of the quantum system is uncertain (100% unknown if state A or B before spin detection). Otherwise, there would be no way to resolve the system to state A or B (collapse). I guess I was wondering if that "must" relationship has already been established, but after reading the article it appears not entirely, which I am very surprised at. The following two quotes makes me think that the relationship was not established as a "must" relationship before and maybe only a partial "must" now:

"Previously, researchers have treated non-locality and uncertainty as two separate phenomena. Now Wehner and Oppenheim have shown that they are intricately linked."

"It would be great if we could better coordinate our actions over long distances, as it would enable us to solve many information processing tasks very efficiently," Wehner says. "However, physics would be fundamentally different. If we break the uncertainty principle, there is really no telling what our world would look like."

I am probably not making much sense. Hope this helps to clarify what I am getting at.

 

[atyy]

Here is the paper referenced by wmikewells:

http://arxiv.org/abs/1004.2507
The uncertainty principle determines the non-locality of quantum mechanics
Jonathan Oppenheim, Stephanie Wehner
Science 19 November 2010: Vol. 330 no. 6007 pp. 1072-1074

In principle, the mathematical structure of quantum mechanics is fully known, and there is in practice no ambiguity in applying the mathematical structure.

The idea of nonlocality, however, is not unique to quantum mechanics. Other theories are possible that are more nonlocal, and yet consistent with (aspects of) special relativity. So why isn't quantum mechanics more nonlocal, since special relativity seems to allow such theories? What additional principles, besides the "no signalling" constraint of special relativity, would lead to quantum mechanics? The paper by Oppenheim and Wehner proposes one answer to that question. They also reference other proposed answers:

http://arxiv.org/abs/0811.3771
Relaxed uncertainty relations and information processing
Greg Ver Steeg, Stephanie Wehner

http://arxiv.org/abs/0905.2292
Information Causality as a Physical Principle
M. Pawlowski, T. Paterek, D. Kaszlikowski, V. Scarani, A. Winter, M. Zukowski

http://arxiv.org/abs/quant-ph/0501159
Implausible Consequences of Superstrong Nonlocality
Wim van Dam

http://arxiv.org/abs/0910.3952
Local Quantum Measurement and No-Signaling Imply Quantum Correlations
H. Barnum, S. Beigi, S. Boixo, M. B. Elliott, S. Wehner

 

[wmikewells]

Thank you for those references. Those articles are probably way above my pay grade, but I will try to get the gist from them.

Just in reading your comments, it appears to be saying that given the uncertainty principle, the specific form of non-locality in quantum mechanics is determined. However, non-locality (as a starting point) does not necessarily lead to the uncertainty principle in quantum mechanics. Is that a good summary?

 

[atyy]

Thank you for those references. Those articles are probably way above my pay grade, but I will try to get the gist from them.

Just in reading your comments, it appears to be saying that given the uncertainty principle, the specific form of non-locality in quantum mechanics is determined. However, non-locality (as a starting point) does not necessarily lead to the uncertainty principle in quantum mechanics. Is that a good summary?

Yes, that's what I understood the article to say also (don't know if it's correct - that's above my pay grade too - I'm a biologist).

 

[DrChinese]

Just in reading your comments, it appears to be saying that given the uncertainty principle, the specific form of non-locality in quantum mechanics is determined. However, non-locality (as a starting point) does not necessarily lead to the uncertainty principle in quantum mechanics. Is that a good summary?

I use the phrase "quantum non-locality" to distinguish it from non-local causality (which is often termed simply as "non-locality"). For example: a measurement on an entangled particle here (your L) definitely leads to an identical constraint on the state of its entangled partner there (your R). That is fully in keeping with the uncertainty principle.

What we don't know conclusively is whether L changes R, or R changes L, or "something else" determines both. After all, the observation outcome is random. On the other hand, ordering of events does not seem to change outcomes.

If something else determines both (as Bohmians believe, for example), then you have non-local causality - and there is spooky action at a distance. There are several other interpretations in which the quantum non-locality is a consequence of purely local operations.

 

[wmikewells]

I use the phrase "quantum non-locality" to distinguish it from non-local causality (which is often termed simply as "non-locality"). For example: a measurement on an entangled particle here (your L) definitely leads to an identical constraint on the state of its entangled partner there (your R). That is fully in keeping with the uncertainty principle.

What we don't know conclusively is whether L changes R, or R changes L, or "something else" determines both. After all, the observation outcome is random. On the other hand, ordering of events does not seem to change outcomes.

If something else determines both (as Bohmians believe, for example), then you have non-local causality - and there is spooky action at a distance. There are several other interpretations in which the quantum non-locality is a consequence of purely local operations.

Is quantum non-locality also "spooky action at a distance" or it is unknown because the collision between L and R might have caused the result? In other words, quantum non-locality is a more generic (spooky or L/R interaction) than non-locality causality (spooky only).

 

[wmikewells]

Yes, that's what I understood the article to say also (don't know if it's correct - that's above my pay grade too - I'm a biologist).

Well, at least you are above my pay grade. I am a business analyst.

 

[bhobba]

Is quantum non-locality also "spooky action at a distance"

Check out Bells theorem:
http://en.wikipedia.org/wiki/Bell's_theorem

Non locality in QM is subtle. Naive reality is, by definition:

1. The idea things only affect things close by - you can't have something in the Andromeda galaxy affecting immediately something here on Earth - such would be called 'spooky' action at a distance.

2. Objects have properties regardless of if they are being observed or not.

What Bells theorem shows is QM and naive reality are not compatible.

The subtle bit is you can retain locality (ie do not have spooky action at a distance) if you abandon the idea of objects having properties unless observed.

Thanks
Bill

 

[wmikewells]

Bill, thanks for the link. I read the link once, but I was not able to get those insights yet. I'll have to read some more and follow some wiki links to get more background.

-Mike

 

[San K]

Is there a hard and fast relationship between uncertainty and entanglement? In other words, if you have one phenomena, you have to have the other. I would think so because of the following example, but I wanted to make sure I understood the relationship. Please let me know if there are better examples or if there is no relationship. There is probably something wrong with my example anyways.

Example: Let's say there are two horizontal electron guns facing each other that fire a single electron each at the same time. The electron from the left gun is called the L electron, and the electron from the right gun is called the R electron. The left gun has a filter on it that blocks all but spin up electrons, and the right gun has a filter to blocks all but spin down electrons. In addition, let's say that there are two electron spin detectors: one above (detector A) and below (detector B) the impending collision. Assuming that the electrons collide and that the detectors will record the electrons spin, there will always be two interpretations of the collision before the spin (and what happened) is determined.

Interpretation 1: Electron L went to detector A and electron R went to detector B
Interpretation 2: Electron L went to detector B and electron R went to detector A

Both are equally probable and there is no certain way to determine which happened until the spins are detected. Because of this uncertainty, the two electrons must be entangled. Otherwise, weird cases would result such as electron R being detected in both detectors and electron L disappearing. Or, one observer seeing one thing and another observer seeing another.

Interesting post...not sure if I got all of it.

However a few things, while I read through the papers mentioned:

1. For entanglement to happen/start -- the particles (or their entangled partners) need to come in contact once.

2. Only about 1 in a trillion tries...do entangled photon emerge...they exit at a certain angle/cone from the crystal ...in case of SPDC (Spontaneous parametric down-conversion)

3. Entangled particles will always have unpredictable values on the property (on which they are entangled)

4. Entangled particles are indistinguishable...as Dr. Chinese mentioned (however this poses a question -- what happens when the photon/electron entangles with the (photon/electron of) detector...)

5. I think what Oppenheim and Wehner (and the paper is good and interesting) are saying is that:

The entanglement "works within" the uncertainty limits.

This uncertainty prevents information to be transmitted (faster than light).

In other words -- if Alice cannot control the uncertainty (say spin up or spin down), why would Bob be able to do it?

After all females (for those who want to impress the prettier sex) are better than males, in precision etc.

5. Below pay grade (i.e. not a physicist) so above might need modifications...lol

 

[wmikewells]

3. Entangled particles will always have unpredictable values on the property (on which they are entangled)

Thanks for the summary. Glad you liked the joke.

I don't even know if my example would be considered a quantum experiment or whether the choice between two pathways (electron L goes up and electron R goes down or vice versa) can be considered a quantum property. I would assume so since position is a quantum property. I don't even know if the collision would preserve the spin up and spin down of the two electrons, so that both spin detectors would detect spin down or both spin up.