Talk:Quantum entanglement/Archive 2

This is an archive of past discussions about Quantum entanglement. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page.

Archive 1

Archive 2

Archive 3

Archive 4

Archive 5

spukhafte Fernwirkungen (spooky action at a distance) - citation?

Almost every article I've read on entanglement (including this wiki entry) contains this quote from Einstein, but I've yet to come across any article that contains a citation of the quotation's original printed source. Does one even exist, or is this just something that Einstein was once heard to say? I actually need to find the original reference for this, so I'm grateful for any illumination.

"pure", "separable", "mixed"

I corrected a small confusion between the definitions of 'pure' and 'separable' states. [from the Centre for Quantum Computation, Oxford]

Do you have a reference? Several books and webpages I have read, on QC and other topics, simply refer to it as a "pure" (as opposed to "mixed") state. For example, Sakurai refers to a "pure ensemble". -- CYD

Hi. Indeed pure states are opposed to mixed states. But both types can also be either separable or not, and that was the confusion that I tried to correct. If a bipartite state (pure or mixed) is separable then its parts can be produced separately by classically correlated sources. If it is not separable, then the state is said to be entangled, and can exhibit non-locality, contextuality and such counter-intuitive phenomena. A review on separability can be found on http://arxiv.org/abs/quant-ph/0006064 but it is quite technical. I again read through and corrected a few problems arising from this confusion.

A comment on notation: The product Hilbert space of the two particles is the tensor product. However, the notation used on this page is traditionally used, at least within mathematical texts, for the direct product, ie the cartesian product of the sets endowed with the appropriate coordinate-wise notions of addition and scalar multiplication. The tensor product is not the same thing, as can be seen by comparing the correctly-given basis here to the basis of the direct product, which would be a sum over one index, extended to include the separate terms individually, but not as a product. This can be a source of considerable confusion for someone who knows a little about the mathematics of Hilbert space and is trying to figure out how it applies to quantum mechanics.

claim that hidden variables theories can't be local removed

Would you care to comment on why this claim is inaccurate? It seems to me a cogent description of the outcome of Bell's theorem. -- CYD

Then Bell's theorem is wrong.

Many-worlds is a counter-example to the claim. It is a purely local theory which is also deterministic. It is also the quintessence of a hidden variables theory; think of all those worlds which we can never observe. I could be wrong about the locality of many-worlds but most people seem to consider it local in the important sense (that non-local effects are unnecessary to explain the Aspect experiment). -- ark

Many-worlds is local, but it is not a hidden-variable theory in the sense of Bell's theorem. I think the characterization of Bell's theorem was correct. See EPR paradox. AxelBoldt, Thursday, May 30, 2002

I don't think it makes sense to talk about many-worlds being "local", because the Hilbert space of a system need not be the space of square integrable wavefunctions. If I'm not mistaken, that's how non-local phenomena (such as the EPR paradox) come about. -- CYD

Whatever you guys decide, the EPR paradox page needs to seriously change. For example, it says "many hidden variables theories have been constructed" and then says "but experiments sided with QM against them". What theories are they talking about? I don't know and it will seem to most people that it's talking about Many-worlds. That's just one example by the way.

Also, an alternative to interpretating Bell's theorem as saying that Many-worlds is not a hidden-variable theory, is simply to say that Bell's theorem is meaningless because it uses a concept of "hidden-variable" which ultimately interests no one. -- ark

Well, obviously that kind of hidden-variable theory interests no one now. On the other hand, EP&R did suggest that quantum mechanics was incomplete, relying on some underlying classical hidden variables. I'm not actually sure if their suggestion was developed by anyone into a workable theory, but Bell's theorem imposes quite strong constraints on the kind of hidden variable theory that can be formulated while matching reality. -- CYD

Something that physicists (and serious physics students) seem to rarely understand is that the mathematics of physics is a completely different subject from the history of physics, which is still different from the ontology of physics (what exists in reality, what I would call the essence of physics).

And they never understand that you can and should teach these three very different subjects separately. So if Bell's inequality is only of historical importance then it's useless and should never be mentioned outside a class on historical physics, where it would be taught aside other great failures of physics. If there's anything in Bell's analysis that's actually relevant to the ontologies of modern physics theories, then that should be carefully extracted out and the rest discarded as chaff. -- ark

As a student of physics (junior level), i'm right now studying the progress of the EPR paradox through Bell's inequalities and into quantum teleportation. I don't think calling Bell's theorem a failure is particularly useful, in that it does set up a specific test of entanglement and present a way to measure it, which was done directly by Aspect, Grangier and Roger. In addition, going though the history of this debate has helped solidify--as much as possible for QM--my understanding of what we're doing with QM. It's poorly worded, but what i'm trying to say is that physics is in some sense inseperable from a selected study of history. it's by learning what other people did, where they were right and where they were wrong, that you actually come to understand what is going on-- for instance, if EPR were right, then QM wouldn't just be incomplete, it would be downright wrong. AGR fround the opposite, and we can work out some more details from there. Talking about quantum entanglement wouldn't make sense at present if you didn't know anything about bell's theorem; that's my opinion as someone looking at the topic for the first time. If you're worried about people misunderstanding how bell's theorem presently applies to physics, well, it seems like directing them to intelligible resources like the appendix of D.J.Griffiths QM book or Bell's Speakable and Unspeakable in QM is the best path to take. This is my first real visit to wikipedia, so please let me know if i have the right idea about how the site works. --T^3

"Entanglement obeys the letter if not the spirit of relativity"

It's funny to read this given:

The peculiar aspects of quantum spin measurements in EPR-type experiments can be regarded as a natural extension of the principle of special relativity. (http://www.mathpages.com/rr/s9-09/9-09.htm)

The "spirit of relativity" refers to the locality principle, which it's fairly clear was what EP&R were concerned about. The link you provided offers an analogy between quantum measurements and relativity - which is not incorrect, but it's not the standard approach to this problem, AFAIK. -- CYD

Of course, the standard approaches don't seem to be a lot of help to most people, especially non-experts, in understanding physics. So I think that, like other ambiguous stuff that you need to be a physicist (and preferably a historian of physics) to understand, it should just be removed. (Like I did on the Copenhagen page. What do you think of it btw?) -- ark

Someone deleted my previous note that at least one scientist has actually used this to transmit information, based on the "fact" that its not possible to do so. Tell that to him--he'd already done it. Classical music, to my recollection. Anyway, here is a formal piece of evidence thats just cropped up:

http://www.theaustralian.news.com.au/common/story_page/0,5744,4522247%255E2702,00.html

The URL's a little mangled...

--Alan D

The URL currently is just dead. Try:

http://www.newscientist.com/article/dn2419-quantum-teleportation-technique-improved.html P0M (talk) 08:28, 23 June 2008 (UTC)

Actually, all they did was quantum teleportation, which never transmits classical information faster than the speed of light, and isn't even helpful for sending classical information. One key paragraph is:

An encoded radio signal is embedded on an input laser, which is combined with entanglement and then scanned. The laser is destroyed in the process. But the radio signal survives and is sent electronically to a receiving station, where within a nanosecond an exact replica of the beam - with the radio signal intact - is retrieved and decoded.

Notice that in order to teleport the laser from point A to point B, they had to first destroy the beam, then send radio waves (at the speed of light) from point A to B, then recreate the beam. You could say that the quantum state was teleported instantly, but the people at B couldn't detect that it had been teleported until after the slow radio waves reached them. Point B didn't end up with any more classical information than was already present in those radio waves. Quantum teleportation has been done by a number of people now, but it has never sent a single bit of classical information. -LC, Sunday, June 16, 2002

OK, I misinterpreted that part...I'm certainly no expert :-) I'm wondering now if the thing on the classical music was the same. He explicitly stated however that he was transmitting information using the technique, but it could have been sensationalistic journalism. I wish I could remember where I saw it.

--alan d

If I'm not mistaken, the reference you provided covers a technique called quantum teleportation, which is not what this article is talking about. The article is noting that it is impossible to transfer information using the EPR setup; otherwise, you would be able to send information faster than light. It is possible to transfer information using quantum teleportation, but then the information will not travel faster than light. -- CYD

I find the first sentence of this article potentially highly misleading: The entanglement of two quantum systems that are far apart does NOT lead to them interacting with each other over the distance - at least not within the standard interpretation of quantum mechanics. They just may show correlations that are so strong that, if you want to explain them in terms of a hidden-variable theory (as EPR intended to, for example), this hidden-variable theory cannot be a local theory. For example, in Bohm's h.v. theory (which agrees with q.m. predictions and therefore, according to Bell, has to be nonlocal) one can indeed see how one of the particles is influenced by what the other one does (which may be influenced by the setting of the other detector). But as you point out yourself, it cannot be used for superluminal communication, because the outcomes are statistical, and on the average there is no mutual influence. Since usual QM only talks about statistical results anyway, it is misleading (at least for the beginner) to imagine a superluminal influence appearing between the particles.

How about something like this: Entanglement is a purely quantum-mechanical property of two particles whose physical attributes (like position, momentum or spin) have become correlated after interacting with each other. The correlations between such "entangled" particles may be shown to be stronger than any "classical-like" theory allows, under appropriate circumstances (see below for more details). -- FlorianMarquardt

I went ahead and did something like this. Feel free to make such changes without posting to the Talk page, as that is more efficient. Welcome to Wikipedia, by the way! -- CYD

On the Formalism section - that's a tensor product of Hilbert spaces, rather than cartesian product, isn't it? I wouldn't want to transgress any conventions usual in the topics, but this does seem to be a key point.

Charles Matthews 10:30, 19 Jun 2004 (UTC)

The assertion made in the article that a given state in entangled IFF its reduced density operators are mixed is incorrect. The correct assertion is this: IF the composite system is entangled, then the reduced operators are certainly mixed. However, even seperable composite states can lead to mixed reduced operators. For example, \Rho_(AB) = \Rho_(A) \TensorProd \Rho_(B) where \Rho_(A) and \Rho_(B) are mixed is a seperable state. However, the reduced density matrices, in this case \Rho_(A), \Rho_(B) are mixed. I had made the change a while back, however it seems to have reverted back. Could somone make the change again?

--Chirag —Preceding unsigned comment added by 61.12.4.26 (talk) 06:08, 17 January 2008 (UTC)

External link may need to be removed

The external link provided at the end of the document titled "Quantum Entanglement For Dummies" I believe needs to be reviewed for credibility and accuracy by someone with a better understanding of this phenomenon. What I find disturbing is the aforementioned site refers the reader to the following article(towards the end just before his appendix): http://www.rednova.com/news/stories/1/2004/08/09/story001.html

From my understanding the author of this article is basing this idea on a gross misinterpretation of numerous facts and quantum entaglement it self. If the author of the page the external link points to found this to be a valuable resource I would question the judgement of that author and the wisdom of linking to this page, and thus indirectly having wikipedia endorsing something which amounts to science fiction.

However, note I have not done this myself. I am an undergraduate physics student and I am recommending that someone with some kind of credentials (better than mine) in this field review my suggestion and remove the link if my supposition is accurate. I feel it would be irresponsible for someone with my level of knowledge in the field to be editing an article on quantum entanglement.

Yes. Please remove it. Unfortunately, however well-intentioned the author of that article may have been, rather than being "Quantum Entanglement For Dummies" that page is "Quantum Entanglement by a Dummy". CSTAR 17:43, 4 Mar 2005 (UTC)

Oh, okay, sorry about that. Guess I didn't do enough checking first. Cal 1234 15:23, Mar 8, 2005 (UTC)

Quantum Entanglement Illustrated

Hi,

The external link provided at the end of the document titled "Quantum Entanglement For Dummies" I believe needs to be reviewed for credibility and accuracy by someone with a

The document has been reviewed by many physicists with good knowledge of entanglement, including: Anton Zeilinger, Lov Grover, Helen Quinn, Anthony Seigmann, and Dr. Amir Aczel. If you'd like more, I can list other people and provide both contact information and their credentials. If you want someone else, then find someone else and e-mail the link. I'd be more than happy to change anything that isn't as technically accurate as it could be (which, by the way, is stated in the document), while maintaining my ultimate goal of having it readable by a general audience.

As far as I can tell by reading the article, in particular the comments attributed to them, saying the article has been "reviewed" by these people is a bit of a stretch. If you can point me to a website where said reviews exist, it would be helpful. Please see comment below about non-functioning link. --CSTAR 21:36, 2 Apr 2005 (UTC)

site refers the reader to the following article(towards the end just before his appendix): http://www.rednova.com/news/stories/1/2004/08/09/story001.html

First, why not ask me to remove the link? It is, after all, just one of many that I read. And, by the way, the page does not say the links are a valuable resource. It merely lists them in an appendix.

Second, you folks seem to forget that many things that seemed science fiction have become science fact. For example, using quantum entanglement for instantaneous communications seemed to be in the realm of science fiction -- Mother Nature was going to keep her secrets to herself. Using adiabatic perturbations of quantum particles, it may be possible to influence the statistics of the radioactive decay in a quantum entangled system.

misinterpretation of numerous facts and quantum entaglement it self. If the author of the page the external link points to found this to be a valuable resource I would question the judgement of that author and the wisdom of linking to this page ...

Powerfully astute logic: Judge the author based a single link, rather than judging the document as a whole. FYI: http://en.wikipedia.org/wiki/Strawman

Yes. Please remove it. Unfortunately, however well-intentioned the author of that article may have been, rather than being "Quantum Entanglement For Dummies" that page is "Quantum Entanglement by a Dummy". CSTAR 17:43, 4 Mar 2005 (UTC)

It's nice to see people being judged and summarily attacked.

However, even if I was a "dummy", this once again judges not the document for its content, but the author. These are two totally different logistical arguments. Do try to keep them separate.

Your referring to potential non-expert readers as dummies is no better (nor worse) than my referring to you the author (who states clearly his non-expert status in the article in question) as a dummy. If this is offensive, then I apolgize, but please change the name of your article. -CSTAR 21:36, 2 Apr 2005 (UTC)

And, for the record, is it too much to ask for a wee bit of maturity here?

Lastly, I noticed on a related page a call for an introduction to quantum entanglement for a general audience, which my document provides. It is not intended to be 100% technically accurate given that it is an ``introduction`` for the masses.

Remember labs in high school physics where wind and friction were not taken into consideration? My document is to get the point across, explain some basic physics, without mucking in technical details. And it does this astoundingly well, thank you very much.

Dave

I'm not going to comment about anything else in this discussion, but I'm fairly certain the following is false:

using quantum entanglement for instantaneous communications seemed to be in the realm of science fiction -- Mother Nature was going to keep her secrets to herself. Using adiabatic perturbations of quantum particles, it may be possible to influence the statistics of the radioactive decay in a quantum entangled system.

I'm not sure if this is referring to the quantum zeno effect, but in any case I'm almost completely certain that you won't be able to use it for instantaneous communications. But I don't see what this has to do with your website being factually inaccurate (or not). -- CYD

CYD,

My statement about stimulated triggering particles for instantaneous communications is partially based on the following:

http://www.arxiv.org/abs/physics/0503052

Their article has yet to be peer-reviewed, however their results look promising.

My main point, however, is that the external link to my site was removed for these main reasons (please correct me if I'm missing some, or have misrepresented them):

The accuracy is in question
There is a link to a related site whose content is quite questionable

I believe having Prof. Anton Zeilinger (http://www.quantum.univie.ac.at/) vouch for the site should be sufficient.

That link doesn't work. --CSTAR 21:36, 2 Apr 2005 (UTC)

The "related" site link in question can be removed quite easily.

Lastly, Google currently ranks me at #2 -- below Stanford and above Wikipedia. I figured adding it to Wikipedia would improve the general understanding of quantum entanglement for the masses. Apparently people disagree. Fine with me. :-)

Have a good one, folks. Sorry we couldn't find a little synergy.

Dave

Umm, the preprint looks to be about plain old quantum teleportation. You can transmit information that way, but not faster than light. -- CYD

entanglement vs. decoherence

Asking "How can I keep these 2 particles entangled as long as possible?" is the same as asking "How can I delay the decoherence of these 2 particles as long as possible?", right?

Yes, that is right. linas 21:36, 5 January 2006 (UTC)

Would it make any sense to merge quantum entanglement and quantum decoherence into a single article?

--DavidCary 18:36, 5 January 2006 (UTC)

Naively, yes; in practice, no. That's because then you'd have one article that's twice as long. These are related ideas, but, already, one can say quite a bit (and more) about each. linas 21:36, 5 January 2006 (UTC)

Contradiction

Currently the article seems to contradict itself. It implies that entanglement *can* be used to transmit information ( quantum cryptography, and perhaps quantum_teleportation ), and yet *cannot* be used to transmit information ("Although two entangled systems can interact across large spatial separations, no useful information can be transmitted in this way.").

Is there some way to clarify that

entanglement might be useful in some communication systems, but
one cannot transmit information faster than the speed of light (whether or not one uses entanglement).

?

--DavidCary 18:36, 5 January 2006 (UTC)

In reply to David Cary, it can be used to transmit information, but not faster than the speed of light.

Say you have two entangled atoms, one which you have flown to the surface of Mars and one which has remained in your laboratory on Earth. You know that the atoms are entangled, that they have a relationship with each other, but what you don't know is their actual state. You also have no way of predicting what their state is. So when you measure the one, you also know what the state of the other atom is through deduction, but as the states of both atoms change randomly over time this does you no good at all - you couldn't use your measurements to control, say, a Mars rover as the only information "transmitted" by measuring the spin-states of atoms sequentially is random noise, in line with causality preservation and the speed limit on information transfer of the speed of light.

It's like the universe works in such a way as to ensure that cause and effect cannot be mixed up, and that is why nothing, not even information about things, can travel faster than light.

--Badnewswade 00:38, 27 April 2007 (UTC)

Actually, it is not Quantum mechanics that holds that..., but it is the Copenhagen interpretation that does so. The statement is less weird than it sounds. The Copenhagen interpretation used to be an empiricist interpretation, shunning metaphysics and being prepared to discuss only measurement phenomena. Measurement phenomena are there only if a measurement is performed. This does not imply that prior to measurement there was nothing, but whatever was there was assumed to be outside the reign of science. Unfortunately, diehard empiricists often interpret this in an anti-realist sense, claiming that there is no reality outside the phenomena. For instance, Pascual Jordan said: before a position measurement the electron was neither here nor there, it got a position only by manifesting itself in a measurement phenomenon. If quantum mechanics is not interpreted in this anti-realist sense but in the more moderate empiricist one in which quantum mechanics is thought to describe only measurement phenomena, I think the problem evaporates. Once more unfortunately, nowadays quantum mechanics is generally interpreted in a scientific realist sense, in which quantum mechanics is assumed to be universally valid and, hence, nothing exists outside the quantum mechanical description. It is funny to observe that scientific realism and anti-realism have the same effect here. This probably is the cause that in quantum mechanics textbooks formulations are often Copenhagen-like although that interpretation has become obsolete.WMdeMuynck (talk) 14:28, 12 January 2010 (UTC)

Shouldn't we rephrase that line to for instance:

Quantum mechanics holds that an observable, for example spin, is indeterminate until some physical intervention is made to measure it.

?

This way at least the reference to "the object in question" (that wasn't mentioned to begin with) is removed. I think this sounds much better. DVdm (talk) 15:45, 12 January 2010 (UTC)

It would be better still to leave out the whole phrase because it unnecessarily introduces interpretation. Entanglement is a property of the state vector, defined in section 2 of the article. It is part of the mathematical formalism of quantum mechanics, having interesting observational consequences in experiments on correlated particles.WMdeMuynck (talk) 23:47, 12 January 2010 (UTC)

I disagree. Mentioning the idea that before the measurement is made there is no set value is an important part of understanding where the controversy about this topics lies. Without it a classical description using conservation laws would be enough. Phancy Physicist (talk) 19:06, 8 June 2010 (UTC)

q. crypto ...

I think that the comment "quantum entanglement is the basis of ... quantum cryptography" is a little too strong - the photon polarisation model of q.crypto doesn't depend on entanglement.

It's possible to use entanglement instead of polarisation to build a q.crypto system, but I don't think it's fair to say it's the basis of it ... (unsigned comment from User:YojimboSan 17 January 2006)

I fail to understand this comment. Aren't the polarized photons entangled? There's no crypto encoding unless both parties receive a message encoded with the same key, viz. a pair of entangled photons. The polarization of a photon is its spin. The details for photon entanglement are ever so slightly more complex than the case for spin-1/2 described in this article, but its essentially the same thing. linas 05:55, 18 January 2006 (UTC)

Not quite, linas. The BB84 quantum crypto protocol only requires polarized single photons to be transmitted, not entangled pairs. The secrecy of the key distribution arises because any eavesdropper increases the polarization noise in the channel. The noise can be detected by looking at the correlations of a subset of the transmitted information. So you always know when an eavesdropper is present. Dave Kielpinski 12:31, 25 January 2006 (UTC)

Ahh. Right, thanks. linas 14:27, 25 January 2006 (UTC)

Suggestion to merge with Quantum coherence

The Wikipedia has articles on Quantum Entanglement as well as Quantum Coherence. Both these are basically the same concept. So there should really be only one article. Unfortunately, at present the two articles do not even cite each other. Even if I am wrong, and the two concepts are not identical, at least they are very closely related to each other. I will look forward to other people's comments on this point. —The preceding unsigned comment was added by 220.227.48.17 (talk • contribs) .

I moved your comment to the bottom to keep it in chronological order, and I added templates to the articles to get more attention. I think Quantum coherence should be merged into this article or Coherence (physics), but I'm not sure which. —Keenan Pepper 23:39, 22 September 2006 (UTC)

minor change

I just added "in general" to the sentence "is impossible, in general, to predict, according to quantum mechanics, which set of measurements will be observed", in the introductory section. This is because if a system is in the eigenstate of an observable, then the quantum mechanics postulates allow to predict the result of a measurement. Oakwood (talk) 00:02, 6 March 2008 (UTC)

Faster than light / instantaneous decoherence aspect enhancement.

LoneRubberDragon (talk) 09:29, 20 June 2008 (UTC)

I understand the aspects of not being able to transmit *information* faster than light, regarding the [no-communication-theorem].

Part 3

3.0 There may be good reasons for the specific wording selected, but the addition of 6 words would help the introductory paragraph below flow better in context. I had to reread the first sentence because it almost conflicted with my no-communication assumptions. So reading backward and forward was a benefit, but it could be refined.

3.1 ((On first examination, observations pertaining to entangled states might appear to conflict with the property of [relativity] that information cannot be transferred faster than the speed of light. But although two entangled systems appear to instantaneously interact across large spatial separations, the current state of belief is that no useful information can be transmitted in this way, meaning that [causality] cannot be violated through entanglement. This is the statement of the [no communication theorem].))

I don't think this emendation is necessarily the best way to fix things. I'm not sure whether it can be backed up with a good citation, but the key difficulty appears to lie in distinguishing between processes that occur in normal space and time, and some kind of influence that does not occur in normal space and time. If a process, e.g., the propagation of light, occurs in normal space then it moves forward at no faster than the speed of light. We do not know what it would mean for an influence to connect the states of the two photons without doing so through space, any more than we really know what it means for the two photons to not be discrete entities but parts of a single event and in some sense the "same" thing. P0M (talk) 07:29, 21 June 2008 (UTC)

As you wish. I do get the gist after reprocessing the article and articles in context, so it is comprehensible after a touch of meditation. LoneRubberDragon 2008 06 21 A 0204

Part 4

4.0 And the following seems to deny the instantaneous probabilistic aspect-decoherence of separated entities (like photon polarization probabilities), and with no-communication-of-information, leaving me confused. I'll let you comment on this paragraph. I understand that the instantaneous influence is probabilistic, which is not an impression, but a fact, otherwise it is subluminal. So it appears the two sentences are entangled to emphasize the no-communication aspect, and not an instantaneous influence impression aspect, so I think I know what you intended, but it could be refined.

4.1 ((The phenomenon of wavefunction collapse leads to the impression that measurements performed on one system instantaneously influence the other systems entangled with the measured system, even when far apart. But quantum entanglement does not enable the transmission of classical information faster than the speed of light in quantum mechanics.))

Possible?

"Quantum entanglement is a possible property of a quantum mechanical state of a system" It is not a "possible property" it is a "property". Every quantum mechanical system of particles has this property (of being able to become entangled). —Preceding unsigned comment added by 89.44.243.118 (talk) 14:35, 29 June 2009 (UTC)

Not everything is entangled with everything, or at least not in any obvious way. When somebody says that two photons are entangled that is a statement about the history of these two photons, e.g., that they were created in one process in a down-conversion crystal. It is also a prediction about future behavior, that if some event "interrogates" one of the photons as to one of its entangled characteristics, a complementary characteristics will be found when the other photon is subsequently examined.

Saying that photons have the possibility of being entangled with other photons is a statement that reflects one component of a full description of photons. It may be an analytical statement because the capacity for entanglement is a consequence of any psi function.

I think that the word "property" in the original statement is not ideal. It suggests that there is something like an automobile accessory that can be added to a photon, and may inhibit the reader from paying attention to the words "quantum mechanical system." Entanglement is something that is a shared state of two or more photons or other such entities. To me, entanglement is a particular kind of modification of the psi functions. It is not something separate that gets attached to two photons like two wedding rings. So it is problematical to use "property" and "state" in the same sentence above.

How about rephrasing: "Quantum entanglement can occur if two quantum mechanical entities (such as photons) are characterized by identical states that are identical superpositions of two psi functions." P0M (talk) 00:57, 30 June 2009 (UTC)

I like to see entanglement in the first place as a property of a wave function of a system of two or more subsystems. If the wave function is not a product of wave functions of each of the separate subsystems it is necessarily entangled, being a linear superposition of such products. Usually subsystems described by such linear superpositions are called entangled.WMdeMuynck (talk) 21:51, 30 June 2009 (UTC)

Can a "subsystem" have only one "component"? In my way of thinking, an asteroid somewhere in intergalactic space (i.e., one with nothing orbiting it and nothing it orbits) would not be a system. A solar system includes, at minimum, a sun and something orbiting around it.

In my experience a system or a subsystem may consist of whatever you like, for instance, one electron, two electrons, a hydrogen atom, two hydrogen atoms, or a molecule, etc. You may have a system of two entangled electrons, the single electrons being subsystems of that system. Or you may have a system of two entangled atoms, the single atoms being subsystems of that latter system. Of course, the whole system cannot always be considered as the sum of its subsystems: still other elements may be involved, like, for instance, the particles mediating interactions between certain subsystems.WMdeMuynck (talk) 13:42, 1 July 2009 (UTCP0M (talk) 18:45, 1 July 2009 (UTC))'

The word "system" comes from a Greek root that means to put things together, and all the definitions of "system" in my dictionary mention or imply a gathering together of parts. So for the sake of the average well-informed reader I think it would be better to speak of systems and their components. A subsystem can be a component of a system, but then the subsystem has to be something with components.P0M (talk) 18:45, 1 July 2009 (UTC)

Is it a sufficient to meet the definition of entanglement for two or more "quantum entities" to have superpositioned wave functions? For instance, if two photons are created by spontaneous parametric down-conversion, does a description of these two photons in themselves stand sufficient? Or do they have to be described as part of the system constituted by the BBO crystal or other device used in their production? P0M (talk) 07:03, 1 July 2009 (UTC)

This is an interesting question that cannot be answered in general. It depends on what kind of measurements you are going to perform. The essential point of entangled states is their description of correlations of measurement results if correlations of the subsystems are measured. If correlations would be measured between the BBO crystal and the two photons, then you ideally would have to consider a three-subsystem's entangled state (although probably in practice entanglement will be unobservable as far as the crystal is concerned). If you do not want to measure correlations between the photons and the crystal but only correlations between the two photons, it depends on the question of whether you are able to distinguish beween different final states of the crystal. You will be able to select photon pairs that are described by a pure entangled state only if such a distinction is possible, because the general two-photon state will be a mixture of entangled two-photon states, the latter corresponding to different final states of the crystal. This subject is dealt with in the theory of conditional preparation. In actual practice, the selection of photon pairs is performed by directional selection of the two outgoing photon beams, taking into account conservation of energy and momentum.WMdeMuynck (talk) 13:42, 1 July 2009 (UTC)

My question was based on my confusion about your earlier paragraph. All I was asking was whether you can validly say that two photons are entangled in some cases.

The original question/objection was purely a question of what "possible property" should mean, and as far as I can tell it was just a question of precision of language. The person with the objection really wanted to insist (at least as I read what he wrote) that any and all "systems of particles" are "able to become entangled." But the original statement did not contradict that statement. It just said the same thing in other words, and did not imply that some state of some system might be impossible to share an entangled state.P0M (talk) 18:45, 1 July 2009 (UTC)

not possible to understand

The text currently has:

For example, when two members of an entangled pair are measured, their spin measurement results will be correlated. Two (out of infinitely many) possibilities are that the spins will be found to always have opposite spins (in the spin anti-correlated case), or that they will always have the same spin (in the spin correlated case). Measuring one member of the pair therefore tells you what spin the other member would have if it were also measured. The distance between the two particles is irrelevant.

What does the "out of infinitely many possibilities" mean here? Are there (1) opposite spins, (2) same spins, (3) some third kind of spins, (4) some fourth kind of spins, and so forth on to infinity?

I have no way of guessing what was in the writer's mind, but to me it looks like one might examine an infinite set of pairs of entangled particles, and find that in each case once one knew whether the particle was an electron or some other kind of particle one would know whether to expect two same-sense spins or two different-sense spins. Following that, one could examine one member of an entangled pair and know by that means what spin the other member of the pair would have.

How should this passage be fixed? P0M (talk) 21:39, 21 September 2009 (UTC)

An entangled state of a two-particle system is an arbitrary linear superposition of products of states of the two particles. Hence, the singlet state of two spins (this is the state in which the spins are strictly correlated so as to have opposite directions) is just one example out of infinitely many possibilities.WMdeMuynck (talk) 20:42, 22 September 2009 (UTC)

But saying that does not imply an infinite number of possible singlet states, no? P0M (talk) 22:00, 22 September 2009 (UTC)

There is only one singlet state for the spins of two spin-1/2 particles.WMdeMuynck (talk)

I think the original statement was unclear for one reason, and adding the part in parentheses made it unclear in another way. Just removing the parenthetical qualification won't fix the problem. I'll try to fix the problem later today. P0M (talk) 15:44, 23 September 2009 (UTC)

You are welcome to do so. I have decided to restrict my contributions to occasionally indicating flaws in existing text (like this one) and giving advice if asked, leaving more elaborate edits to other users.WMdeMuynck (talk) 21:58, 23 September 2009 (UTC)

Your last correction starts from the assumption that entangled spin states are either singlet (spins anti-parallel with certainty) or triplet (spins parallel with certainty), that is, spins are strictly correlated. However, there exists an infinity of other entangled states in which the correlations are not strictly correlated, but that nevertheless could yield violation of the Bell inequalities.WMdeMuynck (talk) 08:58, 25 September 2009 (UTC)

When it says "will be found to always have opposite spins" do you not interpret that to mean "when measured will be found to always have opposite spins"? To me the problem in restating this thing is to distinguish properly between what applies to entangled states and what applies to measured states. Do you contend that the article, as is, is correct? (I self-reverted.) P0M (talk) 23:51, 26 September 2009 (UTC)

Your edit improves the text so as to be not blatantly incorrect any more. On the other hand, the whole paragraph continues to be rather incomprehensible, and remains inaccurate.

First, it is not quantum mechanics that tells us that "observables are indeterminate until such time as some physical intervention is made", but it is the (Copenhagen) interpretation which does so. These discussions are never independent of the interpretation of the mathematical formalism. Most problems and paradoxes of quantum mechanics have their origin in a realist interpretation of the mathematical formalism in which an observable is interpreted as a property of the microscopic object (e.g. [[1]], click `Realist versus empiricist interpretation of quantum mechanics'). In particular, the interpretation of the wave function is generating so many problems that I have decided to give up the realist interpretation in favour of an empiricist one (in which an observable is thought to correspond to a pointer position of a measuring instrument, and the wave function is interpreted as describing a preparation procedure rather than the result of a preparation). I can now answer your question, to the effect that the singlet state represents a preparation procedure in which two spins are prepared to be in such a state that, if a correlation measurement is performed, the pointers of the two measuring instruments will always indicate opposite results.

Second, The singlet state is used in Bohm's version of EPR to explain the EPR problem. It has become a paradigm of the strangeness of quantum mechanics. However, the singlet state is a very special state in which the spins of the two particles are strictly (anti-)correlated. Most states of the two-spin system correspond to a less strong correlation. The unfortunate result of the restriction of the attention to the singlet state is that it is usually forgotten that the EPR situation is quite specific, thus leading to assertions like the one you have corrected.

I think it would be necessary in the present page on entanglement to give first a general definition of entanglement in terms of superposition of product states, without referring to the singlet state. This latter state might be discussed as a (very important) special case.WMdeMuynck (talk) 09:55, 27 September 2009 (UTC)

I just discovered a change in another article that I made about four years ago because somebody else was quite confident that the change was justified, and then I found something in Sears Optics that seemed to say the same thing. So I had just ignored my vague intuition that something was wrong, but actually I was right in the first place and the article was wrong almost from the beginning. My point is just that it is very difficult for me to get things right if I have not had my hands on the real stuff. My constructive visualization powers are better than my memory for things I have seen, but neither is very good. I know I can't do this kind of experiment in my living room, but I wonder whether you know of anything on the subject that is clearly written and accurate. Generally the more sources the better for me, since no one source may have all that I need.

Thank you. P0M (talk) 01:05, 1 October 2009 (UTC)

A clear exposition of entanglement (be it still by way of a simple example) is given, for instance, in A. Peres, Quantum theory, concepts and methods (Kluwer, 2002), section 5-1.WMdeMuynck (talk) 09:51, 1 October 2009 (UTC)

Thanks. I even found it for free, on-line as a PDF from the publisher. It appears to be quite well written. P0M (talk) 21:50, 1 October 2009 (UTC)

Experiment measures "speed" of the quantum entanglement

I've renamed the section to the "Experiment measures "speed" of the quantum non-local connection".