Talk:Quantum decoherence/Archive 1

Relevant Link?
IANAP, but can someone who is confirm or deny the relevance of the link to The Decoherence of Measurement recently added? In particular the following:


 * There seems to be a guiding principle (that of the statistical increase of order in the Universe). This guiding principle cannot be communicated to quantum systems with each and every measurement because such communication would have to be superluminal. The only logical conclusion is that all the information relevant to the decrease of entropy and to the increase of order in the Universe is stored in each and every part of the Universe, no matter how minuscule and how fundamental.


 * It is safe to assume that, very much like in living organisms, all the relevant information regarding the preferred (order-favoring) quantum states is stored in a kind of Physical DNA (PDNA). The unfolding of this PDNA takes place in the physical world, during interactions between physical systems (one of which is the measurement apparatus).

A Google_Test for "PDNA" doesn't show any relevant results but the article itself. CCooke 11:34, 3 Jan 2005 (UTC)

The whole paragraph is simply too vague. YMH 19:53, 9 May 2006 (UTC)


 * Introduuced section on "Decoherence in computation" at suggestion of discussion page of Uncertainty principle.--CarlHewitt 2005 July 6 23:03 (UTC)

I disagree that it is patent nonsense. It looks OK to me up thrugh the section on "Mathematics of decoherence". Maybe just delete after that?--CarlHewitt 2005 July 6 23:32 (UTC)

Perhaps it is not 'a patent nonsense' but link should be deleted. It is 'original research' and has no place in an encyklopedia. It is not an hypothesis either, rather a bit poetic parable. —Preceding unsigned comment added by FrishP (talk • contribs) 12:04, 6 January 2008 (UTC)

Does a parable count as original research? — Preceding unsigned comment added by 46.246.17.38 (talk) 09:05, 15 April 2012 (UTC)

Speedy tag
This is definitely not a speediable article. It looks legit to me, though my physics background is not good enough to work as a hoax detector. I'm pulling the speedy tag - this ought to go through VfD if it's going to go through anything. Denni &#9775; 2005 July 7 00:00 (UTC)

Decoherence in computation

 * Decoherence also takes place in digital computation when a special device called an arbiter leaves a metastable state…

Does this section belong in an article on quantum decoherence? Its use of the term "decoherence" sounds more like macroscopic electronics than quantum physics, unrelated to quantum wave function "collapse". ~ Jeff Q (talk) 02:10, 14 July 2005 (UTC)


 * This is a good question. Leaving a metastable state would seem to have all the right properties of decoherence from a mixed state.  Of couse decoherence is suppose to replace the old "collapse" interpretation.--Carl Hewitt 02:24, 14 July 2005 (UTC)


 * It still sounds like we're confounding two meanings of the term "decoherence". The article on metastability makes no mention of any meaning in quantum physics. "Mixed state" is a very overloaded term; it could be talking about mixed quantum states, mixed electronic states, or mixed state election results. This section sounds quite reasonable — for an article on electronics, not one on quantum physics. ~ Jeff Q (talk) 03:49, 14 July 2005 (UTC)


 * I have added some material to clarify this article and quantum indeterminacy.--Carl Hewitt 14:30, 14 July 2005 (UTC)


 * Well, the updated information is beyond my ability to discern appropriateness. (Based on your résumé, CarlHewitt, it certainly seems within yours.) I guess my biggest problem is that I've never heard of an "arbiter" in electronics, and my attempts to understand the text in terms of macro-scale digital electronics seem to be out of place. When you get a chance, could you come up with an article on Arbiter (electronics) that provides the context for this aspect of digital computation? Thanks for your help. ~ Jeff Q (talk) 05:16, 21 July 2005 (UTC)


 * To start with, I have put some external links in Metastability in electronics.--Carl Hewitt 05:22, 21 July 2005 (UTC)

Lost in Hilbert space ?
Hi all, I rewritten and expanded some areas. In particular I've expanded the intuitive picture of decoherence by trying to make an analogy between Hilbert spaces and ordinary space to explain quantum interference, related decoherence more the various interpretations of QM and linked in density matrices more. See what you think. I haven't touched the maths section -- that probably needs expanding and clarifying as well. --Michael C. Price talk 18:25, 24 June 2006 (UTC)
 * Two new sections. An explanation of decoherence using Dirac's bra-ket notation.  And a section on how decoherence destroys quantum interference.  Based heavily on Zurek's articles as cited. --Michael C. Price talk 00:40, 1 July 2006 (UTC)

The part about the number of degrees of freedom being 3x the number of particles is out of left field and I'm not even sure what the author of the comment meant. If they were implying that spatial coordiantes are the only degrees of freedom of a particle system, that's crazy. I've removed it. Birge 22:31, 12 August 2006 (UTC)
 * You obviously didn't read what the comment said before you deleted it. No relationship between number of degrees of freedom and number of particles is implied in any way.  The other implication you mention is simply fantasy.  --Michael C. Price talk 22:36, 12 August 2006 (UTC)
 * When you say the dimension of hilbert space is three times the number of particles, that's pretty much what you're saying, isn't it? Anyway, I ended up not deleting it and waiting for comment. So, why don't you enlighten me and every other reader of the article as to why the nonrelativistic hilbert space dimension is always three times the number of free particles, or provide a reference or link? Anyway, the whole section is rife with unhelpful parenthetical comments (sometimes a couple of levels deep, which is a terrible grammar) and is in high need of editing. Birge 20:27, 15 August 2006 (UTC)
 * Change "particles" to "free particles" in your first sentence you'll be correct. This is not an easy subject to understand so don't expect any easy explanations:
 * "The dimension d of the Hilbert space is taken to be equal to the number of degrees of freedom of the system"
 * "degrees of freedom in the volume (or equivalently on the dimension of Hilbert space)"
 * "“dimension” in the sense “the number of. degrees of freedom”"
 * --Michael C. Price talk 22:33, 15 August 2006 (UTC)
 * The problem is I think you're wrong, unless I'm misunderstanding what you're saying. The complete state of even a single electron requires an infinite dimensional Hilbert space. Think of the wavefunction representation of a single free particle: that's an infinite dimensional vector space. Out of curiosity: did you write the entire "Lost in Hilbert Space" section? Birge 23:36, 15 August 2006 (UTC)
 * Re single electron: Only if you treat each point in space as a separate dimension/degree of freedom, as is normal in QFT, which is a different sort of dimensionality.  The 3-N aspect only refers to non-relativistic QM, as the article says.  I pretty much wrote every thing under "mechanisms".  --Michael C. Price talk 00:01, 16 August 2006 (UTC)
 * There's really only one type of dimensionality when you're talking about a vector space. And each point in space IS a separate degree of freedom in the wavefunction of a particle. Forget about QED, we're not even talking about that. In the "references" you cited (a problem set is not normally considered a reference) they are talking about finite dimension Hilbert spaces that arise from considering ONLY spin of spin 1/2 particles. This assumes the other degrees of freedom of the particle are constrained or irrelevent. I didn't see a single mention of your 3 dimensions per particle assertion, which is, frankly, ridiculous. I have to ask this, though I'm afraid there's no polite way to do so: exactly what training or qualifications do you have to be making substantial edits and revisions of other's work on the topic of quantum mechanics? You don't appear to really have a solid grasp of any of this.
 * I could ask the same questions of you, since you seem not to have heard of the tensor product. You also seem ignorant of some other rather basic concepts, such as the analogy between classical phase space and a hilbert space.  In non-relativistic QM the wavefunction of an N-particle system is a complex function of the co-ordinates of the N-particles, i.e. over 3N dimensions:
 * $$\psi(x_1, x_2, ..., x_N)$$
 * In classical mechanics a probability distribution in phase space would be a function over 6-N dimensions, since we would include the momenta as well:
 * $$\psi(x_1, p_1, x_2, p_2, ..., x_N, p_N)$$
 * Which part of that do you find so difficult/unbelievable? --Michael C. Price talk 07:13, 16 August 2006 (UTC)
 * (1) In general, there are more degrees of freedom to system of particles than their position wavefunctions (e.g. spin) and (2) You were talking about the dimensionality of the hilbert space. Even if the only degrees of freedom are spatial, that is an infinite dimensional hilbert space. I'm not sure why you're dropping the notion of classical phase space here. It's completely irrelevent to our little argument. Birge 16:18, 16 August 2006 (UTC)
 * (1) Spin is just a discrete-valued label on the wavefunction whereas x or p are continuous variables. Personally I can't see how spin can be conscrued as a contributing a dimension, but it might come down to definitions.  (2) Do you accept that a classical N-particle system with $$prob(x_1, p_1, x_2, p_2, ..., x_N, p_N)$$ inhabits a 6N-dimensional phase space?  If so, how many dimensions do you think $$\psi(x_1, x_2, ..., x_N)$$ occupies?  I think you are identifying the number of eigenvalues = number of basis vectors spanning the hilbert space = dimensions of the Hilbert space, whereas I am using the word dimension in the classical spatial sense.  --Michael C. Price talk 16:52, 16 August 2006 (UTC)
 * Yes, that's exactly the disconnect. The number of basis vectors spanning the space IS the dimension of the hilbert space. So isn't it incorrect to say the dimension of the Hilbert space of a single particle is three? That's exactly what you said in the parenthetical comment that started all of this. Birge 17:11, 16 August 2006 (UTC)
 * Perhaps the term is used to mean different things in different contexts. I refer you back to the links I found that support H'dimension = number of degrees of freedom.  To avoid confusion I'll change the terminology.  --Michael C. Price talk 17:42, 16 August 2006 (UTC)
 * Michael, as I pointed out already, those links referred to systems considering ONLY particle spin, which have discrete and finite eigenvalues. Thus, the degrees of freedom were finite. I'm using the terms "degrees of freedom" and "hilbert space dimension" EXACTLY as those references did. I believe you misread them. Birge 17:51, 16 August 2006 (UTC)
 * Believe what you like, but the facts are this: The first link only mentioned spin after it made the general identification of H-space dimensionality with the degrees of freedom, the second is talking about the holographic principle/Bekenstein bound/black holes and the third is a general paper on geometry and algebra. --Michael C. Price talk 18:10, 16 August 2006 (UTC)


 * Nothwithstanding my previous response, it is obvious that my use of terminology was ill-advised. I believe a helpful change would be to speak only in terms of "phase space" and not "Hilbert space"?  --Michael C. Price talk 18:40, 16 August 2006 (UTC). --Michael C. Price talk 18:10, 16 August 2006 (UTC)


 * Done, and retitled "phase space picture". --Michael C. Price talk 19:34, 16 August 2006 (UTC)


 * Agreed. Birge 19:44, 16 August 2006 (UTC)

I'm uncertain if this is the right place to discus this, but in the phase space analogy section its mentioned several times that quantum decoherence leads to a lack of interference. Would it not be more accurate to say that it leads to a lack of constructive or destructive interference on a measurable or macroscopic scale? Interference is still occurring isnt it? although in a probabilistic way giving the appearance of a classical limit. If what I said is correct or relevant, I feel uncomfortable modifying anything that was said as I am certainly not an expert on the subject. 98.215.254.121 (talk) 08:47, 23 January 2012 (UTC)
 * The loss of interference effects is quite general (i.e. not just of constructive or destructive loss). Yes, there is still very slight interference - but so slight that I'm not sure that it would be helpful to say the microscopic interference persists. -- cheers, Michael C. Price talk 10:33, 23 January 2012 (UTC)

Time and Probabilities
Jerry Heath -

Small particles (at the quantum mechanical level) - if they are independent - are without time; that is, are outside the limits of time.

This does not mean that such a particle can go backwards in time. It does mean that such a particle can be "found" at a given location specified by the probabilities but unrelated to "how fast, how far." Time cannot be involved...the appearance is that the particle could "move" from one place to the other instantaneously (implying if not being infinite velocity).

Note that probabilistic behavior requires that there are no time limitations - otherwise the particle behavior would be required to follow the Newtonian, "how far, how fast" rules. The requirements of time would collapse the wave equation.

But time can be imposed on such small particles. The simple rule is that anything that reduces the possibilities imposes time. The imposition is to the extent that the possibilities are reduced. The limitations of possibilities forces the particle to operate more under "how fast, how far" rules rather than probabilistic rules. Such time based behavior appears to be related to the amount of the limitation of possibilities imposed.

Increasing the density in the region of the particle reduces the possibilities and imposes time. By density I mean the mass over the volume in the region.

Time is imposed on a particle by most measurement methodologies. If time is not imposed directly (the measurement depends on an imposed time limit) it is imposed by increasing the density in order to make the measurement.

Imposing time imposes "how far, how fast" on the particle.

Light in actuality has infinite speed (light has no time). But when we measure the "speed" of light we impose time on the light and determine a finite velocity. This suits our purpose.

Particles will exhibit probabilistic behavior only to the extent that that behavoir is not limited by imposing time on them...since probabilistic behavior cannot occur with "how far, how fast" (time) limits on the behavior.

Time is a contradiction to probabilities. Time collapses the wave equation. - Jerry Heath

ProfJerryHeath 19:29, 28 June 2006 (UTC)

Jerry Heath -

Both the small (quantum) particle and the distribution probabilities of such a particle cannot be in time. The distribution must form immediately and the particle cannot have time. The particle 'obeys' the distribution curve immediately.

But as we view such particle probabilities our view is limited by time because we are 'stuck in time.' Thus as we measure a timeless phenomena our time world imposes a time on the measurement. But the time impression we get is a phantom of timeless probabilities. The collapse of the wave equation due to density is also a result of this kind of process. Time and probability are mirror worlds.

Gravity is a special distribution that has time associated with it. As gravity becomes an important force, due to density, the probability distribution collapses into the time mirror of probabilities.

Because we are 'stuck in time,' when we look at quantum processes we can only see them though the looking glass. Schrödinger’s cat is placed, philosophically, on the other side of that looking glass. - Jerry Heath

12.162.215.130 13:44, 11 July 2006 (UTC)

Huge reversion
I'm really sorry, but it appears that the user Michael C. Price has been making huge revisions to this article that are entirely and utterly incorrect. His edits are often plausible and borrow from correct notation, but are gibberish upon close review (such as nice looking dirac notation equations which multiply two ket vectors together, a meaningless operation in the context of quantum mechanics). Pleaser refer to my discussion with him below, as well as his user page for more examples of his run ins with other physics pages. If somebody knows the correct procedure for handling what amounts to a dedicated and repeat vandal, please help. I'm not sure what to do, but cranks like this are completely destroying the integrity of Wikipedia as they have far more time on their hands than the people who actually know science. I can't think of a good way to filter out the good edits from his bad ones (and many of the good edits were on technically incorrect entries made by him) so I've reverted to the last version several months back before he started taking over this article. I'm sure Michael will revert this revert, but we really need to do something about this. I don't have time to deal with this any more. Birge 03:13, 16 August 2006 (UTC)


 * I think rather the problem comes from technically ignorant authors who revert first, ask questions later. And then pronounce as "gibberish" operations which
 * multiply two ket vectors together, a meaningless operation in the context of quantum mechanics
 * Have you never heard of tensor products? --Michael C. Price talk 06:53, 16 August 2006 (UTC)
 * Yes, I know what a tensor product is, and you didn't write it as a tensor product. Birge 15:12, 16 August 2006 (UTC)
 * I didn't write it as "multiply" either. I was assuming a basic level of intelligence from the reader to realise that tensor product was implied by the use of, and link to, Dirac notation.  Obviously I didn't dumb down enough and for that I apologise.  --Michael C. Price talk 15:22, 16 August 2006 (UTC)
 * You're right. Looking back your notation is consistent. I was wrong and just saw two kets back to back and didn't look closely enough to see what you were doing. I take back that objection and apologize. Birge 15:33, 16 August 2006 (UTC)
 * I appreciate the retraction and amicable resolution -- not something you often see. Thanks!  --Michael C. Price talk 15:49, 16 August 2006 (UTC)
 * Whoops. I just checked out the Dirac Notation page, and apparently ket ket is an accepted shorthand for the tensor product of two states. Again, I'm really sorry. I should make it clear here that I very much apologize for calling you a crank, not just for my criticism of the dirac section. Birge 19:47, 16 August 2006 (UTC)


 * Heh, i hope other editors learned something from this little incident and its resolution; I did :) --bonzi (talk) 13:30, 8 January 2009 (UTC)


 * That humans are essentially good? ... said: Rursus ( m bork³ ) 13:39, 12 January 2010 (UTC)

Questions on Dirac Section
Ok, I'll try to deal with this more productively and in the spirit of wikipedia. In the Dirac section, there is the statement that unitarity of the evolution leads to orthogonality of the |E_i> states. Then, later, it's stated that decoherence makes them approximately orthogonal. This doesn't make any sense. The |E_i> are states that are defined. Either they are orthogonal or not, and they don't change upon evolving the system. (I.e. if a system starts in |E_1> it may evolve to be a superposition of other states, but |E_1> is a mathematical definition that doesn't change.) - Birge 16:11, 16 August 2006 (UTC)
 * Okay, I see the source of the confusion. $$|E_i>$$ has different definitions in the two interaction categories defined.   $$|E_i>$$ in one section is $$|i,E_i>$$ in the other.  It is the joint total states (environment + object system) on which orthogonality is exact.  The states on which the orthogonality is only approximate are subsets of the joint system (environment - object system).  I'll revise to make this clearer.  --Michael C. Price talk 17:14, 16 August 2006 (UTC)
 * For the moment I've left the two different uses in, but put them in different subsections. --Michael C. Price talk 09:48, 17 August 2006 (UTC)

Fair enough. I think another problem in the section is that the entire point of the formalism is this business of einselection which is somewhat glossed over. It's just stated as fact that we are able to pick a basis in the system that will end up evolving to yield these |E_i,i> states in the combined system, and I think some explanation of that is needed. I suspect that's really where the subtlety of the theory comes in.

If I may: isn't a key point in all this that the orthonormality of |E_i> can be *derived* from classical QM? If correct, then the article would be improved by simply stating this fact for the reader. (I am not familiar with the term einselection, but infer it is the phenomenon in which this orthonormality of the |E_i> states occurs.) --Randall B. Smith, January 2008 —Preceding unsigned comment added by 74.2.65.26 (talk) 08:22, 27 January 2008 (UTC)


 * Einselection has its own article, so any specific points might be better raised on its virgin talk page. In general, though, you can always pick a basis in quantum theory -- indeed that's what, I suspect, some people don't like about QM, that it seems just too easy to pick a basis. --Michael C. Price talk 20:20, 16 August 2006 (UTC)
 * I agree that you can pick any basis you want, I'm just saying the notion that you can pick one that has such nice properties upon interaction with the combined environment system is not obvious. Perhaps you're right that it belongs on the einselection page. However, given that it's the kernel of the entire subject of decoherence theory, I'd say it warrants more explanation here. Birge 20:32, 16 August 2006 (UTC)
 * Oh, one more thing. I think there's a missing definition for what |k(i)> refers to. It seems like it's suppposed to be some subspace basis set in the complete system, but I think it needs to be defined. Birge 20:58, 16 August 2006 (UTC)
 * Yes, I just noticed that myself. Carry on listing the problems and I'll try to get back tomorrow.  --Michael C. Price talk 21:08, 16 August 2006 (UTC)
 * Okay, problem solved by deletion -- it was irrelevant (and confused and probably wrong OR!). Also I've updated einselection to include what seems to be its defining characteristic, namely the orthonormality of the environment states, with a direct quote from Zurek. --Michael C. Price talk 09:48, 17 August 2006 (UTC)

environment effected in Dirac Notation
I am attempting to familiarize myself with what's going on here, and the following statement has me wondering if the wrong word is being used. Under the section, Dirac Notation, the following sentence appears:

There are two extremes in the way the system can interact with its environment: either (1) the system loses its distinct identity and merges with the environment (e.g. photons in a cold, dark cavity get converted into molecular excitations within the cavity walls), or (2) the system is not disturbed at all, even though the environment is effected (e.g. the idealised non-disturbing measurement).

I suggest that the phrase, "the environment is effected" be changed to "the environment is affected", as I don't believe the intent is to communicate that the environment is created by the system being discussed, but that the environment is influenced or altered by that system. -douglas


 * I copped out and changed it to "disturb". --Michael C. Price talk 06:14, 23 November 2006 (UTC)

One article too many?
Why do we have separate articles for quantum coherence and quantum decoherence? Borisblue 00:19, 30 November 2006 (UTC)


 * Because they are not the same thing, nor are they opposites or converses. --Michael C. Price talk 00:53, 30 November 2006 (UTC)

Measurement Problem
@Michael C. Price: Why did you remove the incompleteness claim? The paragraph mentioned explicitely, that in order to solve the measurement problem of the CI, decoherence must be supplied with some nontrivial interpretational considerations. This implies, that the incompleteness claim is not valid for all interpretations. The original statement was therefore completely correct.--Belsazar 15:45, 3 September 2007 (UTC)
 * The discussion is not limited to the CI. Also MWI claims that interpretation proceeds from the formalism: thus the incompleteness claim is not valid for all interpretations (and MWI in particular).--Michael C. Price talk 00:54, 4 September 2007 (UTC)
 * Also MWI claims that interpretation proceeds from the formalism -> This claim of MWI is a nontrivial interpretational consideration per se and rather supports the statement in the article.--Belsazar 09:05, 4 September 2007 (UTC)
 * I'm not sure what you mean (you seem to contradict yourself), but the claim that the MWI emerges from the formalism alone is one made explicitly by Bryce DeWitt. It is a non-trivial exercise to show this, but that is another matter. --Michael C. Price talk 09:15, 4 September 2007 (UTC)


 * I have mixed feelings about this, but I tend to side with MichaelCPrice, for somewhat different reasons. The measurement problem in plain quantum mechanics often gets discussed as a philosophical issue, but you can phrase it in purely operational terms: when measurements have a detectable effect, and there's no definition of what constitutes a measurement, you can't predict the behavior of any system in which a measurement might take place. The sorts of people who complain about the measurement problem generally have that fact in mind. Decoherence does solve that problem, by making the supposed difference in behavior so tiny that it's way beyond anything even in principle detectable. All that's left of the measurement problem is metaphysics. So the claim that decoherence doesn't solve the measurement problem seems like vague and somewhat dubious philosophy, whereas there seems to be a clear scientific sense in which it does solve it. -- BenRG 09:37, 4 September 2007 (UTC)


 * For me the issue is now solved by the clarifications in the article (even if the claims of DeWitt sound somewhat strange to me, but this is another issue). Thanks @Michael C. Price.--Belsazar 12:07, 4 September 2007 (UTC)

(Geoff) I added an excerpt from "Decoherence, the measurement problem, and interpretations of quantum mechanics" about how quantum decoherence explains the transition of a entangled state to an ensemble of pure states but doesn't actually explain the step where a measurement is carried out and a single state results. I know this was a confusing point for me since the intro says that decoherance explains apparant wavefunction collapse, but if you check out the math the resulting state after decoherence is still a superposition, just not an entangled one.
 * This addition seems to be repeating points already made. And the lead is too long. --Michael C. Price talk 20:36, 17 September 2009 (UTC)

The statement "decoherence does not attempt to explain the measurement problem" is unsupported, and in fact contradicted by the measurement problem topic itself. While there is some dispute as to whether it does in fact explain quantum measurement, there is little doubt that it attempts to. Joncolvin (talk) 21:02, 18 April 2021 (UTC)

"decoherence does not solve the measurement problem" is contradicted by the entry in the "measurement problem" topic. Changed it to "there is controversy whether..." Joncolvin (talk) 21:14, 18 April 2021 (UTC)

The lead
Is it possible for the first paragraph to be phrased in a way that is at all comprehensible to readers unfamiliar with the underlying topics?

--Ultra Megatron (talk) 01:47, 20 November 2007 (UTC)

It is very difficult for any information about quantum theory to be phrased such that anybody "unfamiliar with the underlying topics" will find it easily comprehensible. While I enjoy reading wiki articles about quantum physics and theory, I will never learn all about the subject from this source. No one should expect to. The subject matter is so complicated that simplistic introductions to even small(ish) parts of it seem to be problematic at best. Can it be clearer? I would hope so, but until an Alan Guth or Brian Greene comes along to make it all a little clearer, we will have to muddle through.

-- The lead in us completely unacceptable, vague, and poorly written. It is a cop out to claim that information about Quantum Mechanics is necessarily incomprehensible, poor writing makes it incomprehensible. I have a rudimentary grasp of decoherence from my professional life, but the intro paragraph left me scratching my head. A proper introduction should be as clear as renormalization is, by giving context, general reason for inclusion, and a basic definition. While the entire article is poorly written (anytime an author appeals solely to the mathematics for a "description", it is inappropriate for wikipedia), at least the opening can be clarified in a timely manner. —Preceding unsigned comment added by 68.190.80.137 (talk) 14:52, 1 January 2008 (UTC)

-- I agree the opening paragraph could be improved. I suggest something like this: ''Quantum Decoherence is a phenomenon that occurs in classical quantum mechanics. It is exhibited by a quantum mechanical system interacting with its environment in such a way that the phenomenon of quantum interference becomes negligibly small. Calculations suggest that in most situations quantum decoherence will occur very rapidly, and that one must go to great lengths to carefully prepare a system and its environment if one wishes to avoid the phenomenon. Quantum decoherence is especially significant for two reasons: 1] it can explain why we normally observe systems that obey classical laws of probability, and 2] why wave functions appear to collapse.'' I don't have references at hand for the few places in there that could use them, but if anyone thinks this prose merits inclusion, I'll try to dig them up. Also would need to link-ify all the appropriate terms. (Randallbsmith (talk) 08:58, 27 January 2008 (UTC))
 * I suggest removing "Calculations suggest that ".--Michael C. Price talk 13:35, 27 January 2008 (UTC)


 * I agree that the lead is completely unacceptable. The proposed lead above is far superior from the standpoint of being more easily understood. This is not my area, but an intelligent reader should be able at least to get some vague inkling of what the topic is about from the first few sentences, not read long sentences filled with unexplained jargon that's completely opaque. Because the proposed lead above ends with the concept of wave function collapse, what do you think of adding a simplified parenthetical explanation: "(the reduction of the physical possibilities into a single possibility as seen by an observer)" or something like it? (This explanation is in the Wave function collapse article.) - Do c  t  orW  04:53, 3 March 2011 (UTC)

Entropy
Would it be possible to add a discussion on the effects, or otherwise, of decoherence on the entropy of the objects and the resulting combined system?

The article mentions that the process of decoherence is irreversible. Can I presume that this is "irreversible" in the statistical mechanics sense of "it is in principle reversible, but unimaginably vastly hugely improbable that it might reverse". -- 80.168.224.193 (talk) 10:16, 30 December 2007 (UTC) Irreversible in thermodynamics is a technical term. Reversible processes are quasi-stationary, and always close to equilibrium. While related, it not same as Zermelo's objection to Maxwell's theory, known as the Wiederkehreinwand. FrishP (talk) 11:49, 6 January 2008 (UTC)

Irreversibility
Yes, decoherence is "irreversible" in the (quantum) statistical sense. It is the mechanism by which the "quantumness" of a system is transferred to an environment, which is treated statistically. If we did not treat the environment statistically (i.e., we kept track of everything), we would not get decoherence to mixtures. Gamblorius (talk) 18:42, 9 March 2008 (UTC)

Reversibility and Irreversibility
John von Neumann's Mathematical Foundations of Quantum Mechanics presents an interesting discussion of this question in ''chapter V, "General Considerations, 1. Measurement and Revesibility". ''

According to von Neumann's analysis, there are two quantum processes relevant:

Process 1: measurement (collapse of the wavefunction) and

Process 2: reversible time evolution according to a time-dependent Schrödinger equation.

Wavefunctions of the system, measuring device, and environment evolve reversibly according to process 2. Process 1 entails irreversible collapse of the wavefunction into a statistical mixture. According to von Neumann page 357 "[process] 2 transforms states into states while [process] 1 transforms states into mixtures".

von Neumann goes on to say (page 398),"Although our entropy expression, as we saw, is completely analogous to classical entropy, it is still surprising that it is invariant in the normal evolution in time (process 2) and only increases with measurements (process 1)."

Decoherence is not the same as collapse of the wavefunction (process 1). If decoherence occurs by evolution of a time-depenedent Schrödinger equation (process 2), then, in the context of von Neumann's analysis, decoherence is not irreversible. von Neumann extends his idea of process 1 to macroscopic examples.

A discussion of how decoherence and measurement, subjective or objecitve, may lead from "one quantum world" to an ensemble of "many classical worlds" is given in Stapp H. P., Physical Review A, 46(11), 1992.

Joseph Alia (talk) 02:00, 3 May 2008 (UTC)

Could use refs.
Could use references to Planck's length and Planck's time. 71.175.15.74 (talk) 06:23, 2 November 2008 (UTC)

Criticisms section
This section currently makes a big deal about points made elsewhere in the article, namely that: These are not weaknesses of decoherence, but features of the interpretational nature of QM. This section seems to completely miss the point about decoherence, namely that decoherence produces the appearance of collapse and never claims to do anything else. --Michael C. Price talk 13:15, 5 November 2008 (UTC)
 * 1) Environmental decoherence does not produce a collapse of the wavefunction.
 * 2) Does an isolated quantum system ever collapse to a classical state?

I've tried to explain the issues a bit more clearly in the article. I suggest that we delete this section, since it is totally confused -- although the reference could be salvaged. --Michael C. Price talk 13:34, 5 November 2008 (UTC)

Dear Michael,

It is not a matter of interpretation and the fact that these questions are seen in this way means that some conceptual foundations of quantum mechanics are missed. All the point relies on where to put the border between a classical and quantum world. Environmental decoherence invokes an external agent and this is not at all completely satisfactory. This is an essential point that seems totally missed here. Also the fact that some people that wrote this article claims that decoherence gives appearance of a collapse are not correct. When you have a density matrix that is just a sum of probabilities you have no collapse at all. The question of an isolated or closed system and appearance of a classical world is not a matter of interpretation but something that can be put at test through experiments. Indeed, one of the main problems environmental decoherence has to face is cosmology. The fact that an article like this is written without any criticisms, claiming that problems are all solved it is something that worries me but that I can see today in a lot of fields of physics.

The appearance of a collapse is not enough to solve the measurement problem in quantum mechanics. Indeed, if a border exists between the classical and the quantum world one could accept Copenaghen interpretation and this is where the heart of the problem lies.

Anyhow, my view may be proved wrong in the near future, that is environmental decoherence is just partially true, so you can decide what you like about this article.

Marco
 * Hi Marco,
 * you say "Environmental decoherence invokes an external agent and this is not at all completely satisfactory." I wouldn't use the word "invokes"; I would rather say that decoherence uses the fact that systems often have very many degrees of freedom, and that this has many important consequences.
 * I don't know the basis for your objection to the claim that decoherence explains the appearance of wavefunction collapse (your statement above about the density matrix and the sum of probabilities not mimicking collapse needs more explanation). However the claim that decoherence does explain the appearance of collapse is one that is widely claimed in the literature (and one that I'm happy with).  If you have a peer-reviewed counter reference, then we can include it, but the criticism section as it is seems hopelessly muddled on the subject.
 * I agree with your statement that "The appearance of a collapse is not enough to solve the measurement problem in quantum mechanics". To solve that we always need to adopt an interpretational stance.  Where does the article claim otherwise?  Your criticism of decoherence seems to imply that decoherence solves the measurement problem, which it doesn't (although it does throw light on the matter). --Michael C. Price talk 22:37, 5 November 2008 (UTC)

Dear Michael,

Thanks a lot for your answer to my comments. I used to think that the struggle some people is fighting to improve our understanding of how reality forms was somehow known in the community. The reference I put in the article was due to one of this person, Mario Castagnino that uses Riemann-Lesbegue lemma to recover classical world from a closed quantum system. By my side, I prefer to analyze the strict connection that exists between quantum and statistical mechanics and I have shown in a series of papers how thermodynamics limit can be used in a closed quantum system to recover the classical world. So, your observation that internal degrees of freedom may drive the system toward classicality is correct but, let me say, it must be proved and implies a new physical effect!

Aside from other works, mine are the following:

http://arxiv.org/find/grp_physics/1/AND+au:+frasca_m+ti:+decoherence/0/1/0/all/0/1

This gives an hint of my view about and also on all the experimental work on this matter. Currently I have moved my field of activity to particle physics but I follow all these studies with much interest.

I have seen that you are working at Imperial College. I have had the luck to meet Peter Knight to some conferences and he took a picture of me some years ago. I have no more chance to meet him but surely you can take my best greetings to him.

Thanks.

Marco —Preceding unsigned comment added by 213.156.50.160 (talk) 08:31, 6 November 2008 (UTC)

I agree with Michael that this section is confusing, as the two points are hardly criticisms. At lest I was confused when I read it. A criticisms section is important, so please place some real c criticisms here. It was the first section I read beyond introduction. Shengchao Li (talk) 20:36, 24 February 2009 (UTC)
 * Deleted section -- too much duplication with rest of article and lack of clarity. When we get some good references and a coherent summary of them perhaps we can recreate the section. The one reference there was is now listed under "further reading". --Michael C. Price talk 09:34, 25 February 2009 (UTC)

Non-unitary?
All physical processes are fundamentally unitary. The appearance of a statement Decoherence is a non-unitary process by which a system couples with its environment is highly misleading. It is also to much detail for the lead. --Michael C. Price talk 22:51, 30 November 2008 (UTC)
 * Clarified the non-unitary claim, and moved most of the text from the lead to the appropriate subsection. --Michael C. Price talk 12:01, 11 February 2009 (UTC)

Quantum Entanglement
There needs to be a section noting the relationship to Quantum entanglement. In quantum entanglement, some controlled event causes two entities (such as electrons) to have one or more state values (such as spin angle) be mutually dependent (such as, if one electron has spin (+) then the other electron must have spin (-)). The observable value of one is causally linked to the observable value of the other. While an observation of either entity can yield any value allowed by quantum mechanics (such as spin (+)), subsequent observation of the other entity will always yield the associated required value (in this case, (-)). Any interaction of either entity with anything else (such as being observed) causes the states of both entities to `decohere'. The observation of the state of one entangled electron can be compared to an observation of the state of the other entangled electron, but at this point, the states of the two electrons have undergone `decoherence' and the entanglement is lost. Michael McGinnis (talk) 21:02, 28 April 2009 (UTC)
 * I suppose we could say that decoherence converts quantum entanglement into classical correlations. That what you have in mind? --Michael C. Price talk 12:52, 29 April 2009 (UTC)
 * That is a good suggestion. It might be good to include a note that the information of the correlation (entanglement) cannot cease to exist, but that decoherence is merely an irrevocable loss of the context of that information, which is retained as entropy. -- Michael McGinnis (talk) 20:19, 29 April 2009 (UTC)
 * Yes, that sounds like a good way of expressing it. --Michael C. Price talk 20:54, 29 April 2009 (UTC)

There is a fundamental objection here .. IF measurement of one spin causes decoherence for both of the entangled pair, then information (that decoherence has occurred) now has to travel instantaneously (i.e. faster than light) to the other one of the pair. IF measurement of one does not cause decoherencece of the second (or if information does not travel faster than light), then there is a 50% probability that when the second decoherence event occurs the SAME spin will be found. — Preceding unsigned comment added by 62.3.239.168 (talk) 23:16, 29 September 2011 (UTC)

Notation
This article contains the statement

$$   |i \rang |\epsilon\rang $$ evolves into $$|\epsilon_i\rang $$

But to my limited understanding of quantum mechanics, this doesn't make sense -- you can't multiply a ket by another ket to get a ket. Could someone more knowledgeable please change it into the standard notation for this situation, whatever that is?

Nathaniel Virgo (talk) 17:13, 18 August 2009 (UTC)
 * Kets from different systems can be multiplied together.--Michael C. Price talk 17:19, 18 August 2009 (UTC)


 * Ah yes, I see. I must have been having a bad brain day.  Perhaps it could be made slightly less confusing by using the tensor product symbol explicity? i.e.


 * $$   |i \rang \otimes |\epsilon\rang $$ evolves into $$|\epsilon_i\rang $$


 * this would have to be done consistently though. I'll leave it to more experienced people to decide whether that's necessary. Nathaniel Virgo (talk) 19:18, 3 September 2009 (UTC)

The problem, however, remains. First aspect: No, kets cannot be multiplied together. When we have a vector $$a$$ from a first Hilbert space $$H_1$$ and a vector $$b$$ from a second Hilbert space $$H_2$$ then we can form a tensor product of the Hilbert spaces, namely $$H_1 \otimes H_2$$ and in this Hilbert space the vector $$a \otimes b$$ can be formed. However, this is not an operation on two objects which form a third object (as in $$2 + 3 = 4$$ where all involved objects are in the same set of natural numbers) but we have an operation which takes on object in one set another object in another set and we get an object in a completely different, new set. Second aspect: The problem here is that it is nowhere seen from which Hilbert spaces the vectors are taken. Of course, $$ |i \rang |\epsilon\rang $$ or $$   |i \rang \otimes |\epsilon\rang $$ can be formed and it is a vector in a third Hilbert space. The notation $$|\epsilon_i\rang $$ however is maximally confusing, since it merely introduces a fresh notation and in this sense is completely void unless an independent meaning is given to this notation first in a mathematical or physical sense (and this is lacking here). — Preceding unsigned comment added by 217.95.169.241 (talk) 10:53, 5 September 2018 (UTC)

History section ?
I think the article would be enhanced by a section on the history of the term, development of concepts, and of contributors to work in this area. Any volunteers?CecilWard (talk) 14:05, 10 December 2009 (UTC)

There is a link to http://en.wikipedia.org/wiki/H._Dieter_Zeh in external links but no mention of what I learned In Max Tegmark's 2014 book "Our Mathematical Universe". Max had once thought he had discovered it and while thinking of a name for it he discovered that: "In fact, I soon learned that the German physicist Dieter Zeh had discovered the effect already back in 1970." Because of his special insight could we ask Max to polish up this section?

I'm 1st year Physics at Sydney University, so I have no expertise on the subject but wanted to argue for a Decoherence page that starts with a good definition of what it is now as a subject of study, in context with its genesis from http://en.wikipedia.org/wiki/Hugh_Everett and http://en.wikipedia.org/wiki/H._Dieter_Zeh, the following decades of dormancy in contrast with its more rigorous recent uptake, possibly having some bearing with decline in belief with the Copenhagen interpetation. A concise opening that most experts can agree on, followed by an index. Neither page Decoherence or Coherence does this well at the moment. Andrewboychurch (talk) 22:59, 28 June 2014 (UTC)

Gravity-induced decoherence
"Fundamental decoherence", "Intrinsic decoherence". Worth mentioning? Googling it gives a bunch of links to peer-reviewed articles. I.e.: --Dc987 (talk) 22:17, 14 December 2009 (UTC)

Bohm victory?
This is not a proper talk page question, but does the current popularity of "Quantum decoherence" actually imply that Bohm's interpretation temporarily have "won" before the Copenhagen interpretation? ... said: Rursus ( m bork³ ) 13:43, 12 January 2010 (UTC)

Hoping to improve readability/add plain-language descriptions
I am announcing my intent to make this article more readable by non-experts. I think the bulk of what is here now is masterfully written, and I know it is a very difficult topic to correctly explicate - because so much of what has been said by those attempting to simplify the topic is flatly wrong. However; a recent comment from a friend about the difficulty he had making sense of this article (his words were stronger) prompt me to make some attempts at plain-language descriptions.

I am no expert, when it comes to the Math especially, but I have communicated with several experts on this subject - including H.D. Zeh, Erich Joos, and Anton Zeilinger. Between correspondence, lecture attendance, and face to face conversations, I've learned a lot about this topic most people don't get to learn or ask about. And apparently; I do understand some of the subtleties of the Math used in decoherence theory better than individuals who raised objections above. At the very least; I have a pretty clear idea of what decoherence is not.

My entry in the current FQXi/Scientific American Physics essay contest, entitled "The best of both worlds," includes a fair amount of discussion on this topic, and introduces some of the descriptive metaphors I plan to use in this article. I am hoping my expertise at conveying highly technical topics to non-experts will be of help here.

Regards, JonathanD (talk) 22:14, 7 March 2011 (UTC)

New paragraph added in lead
In an effort to make this article more readable, I have added a paragraph using the metaphor of ocean waves encountering the shore or a vessel - which makes them appear as discrete entities. Hopefully this is the right place to insert this content, so that people who are not QM experts will read further.

Regards, JonathanD (talk) 05:57, 8 March 2011 (UTC)


 * Is it really necessary to open five sections all saying the same thing?
 * Anyway, the tsunami metaphor doesn't work for me. There must be a better metaphor, probably involving heat since it is a thermodynamic phenomenon. -- cheers, Michael C. Price talk 05:31, 11 June 2011 (UTC)


 * Please stop opening new talk page sections all the time.
 * I think the "metaphor" in the lead should be moved to its own section. There should not be stuff in the lead (see WP:LEAD) that is not expanded in the main body.  (There is also the problem that this metaphor is unsourced and devoid of links,  but I can live with that if it is not in the lead.)-- cheers, Michael C. Price talk 07:22, 12 June 2011 (UTC)


 * The first external link contains a very good explanation of decoherence, technical and non-technical.  Suggest we just point to this. -- cheers, Michael C. Price talk 07:43, 12 June 2011 (UTC)
 * Done. -- cheers, Michael C. Price talk 05:23, 18 June 2011 (UTC)

Lead section readability edits complete
I am announcing that I am pretty much done here, for now. I have added a paragraph and a few brief sentences to the lead, which provide some plain-language explanations. I'm leaving the tag up "This article may be too technical" until I get some feedback, or until I decide it's the right thing to do.

Honestly; I think the technical writing in the details of individual sections is top-notch, but I can see why it got tagged. Unfortunately, it really is a difficult subject to understand without some Quantum Physics background. Even then; too many people learned QM as an exercise in statistics and probability, because the Copenhagen interpretation encourages folks not to dig too deep into the fundamentals.

But since I've been privileged to have some of the fundamentals get explained to me by experts, I'm hoping my grasp of the fundamentals for this topic is adequate to the task of making the basic concepts of decoherence understandable. I'll check back here from time to time, to receive any feedback. I may do some more minor edits, but my immediate task is complete.

Regards,

Jonathan - JonathanD (talk) 01:37, 9 March 2011 (UTC)

This article is fine.
You can Get rid of the 'make this article simpler' tagline. I understood it just fine - You can't make quantum mechanics simpler anyways. You either understand it or you don't. —Preceding unsigned comment added by 131.151.185.39 (talk) 01:58, 29 April 2011 (UTC)

Reverted to May 27 and removed 'too technical' tag
I did a reversion to re-instate plain language description in lead beginning "A useful metaphor..," then removed the 'too technical ' tag. I checked the description in that para with a couple of experts and they said it was quite appropriate. It's true that the wavefunction is not the same as ocean waves, which are a Classical phenomenon. But if a non-technical description is needed, that one serves well. Consider the following explanation.

When a tsunami occurs, it may strike a particular location, and thus be viewed as a discrete event at that location. However; the same wavelike phenomenon will persist for some time - as a wave or coherent group of waves - to show up as another discrete event on each of various islands, and eventually on the other side of the ocean. So; while the tsunami will lose its force and 'decohere' completely over time, the wavelike nature is indisputable. It is a global wave with discrete manifestations at various points on the globe.

I would be happy to discuss this further, if someone has the courtesy to state any objections. If my attempts at providing an accessible description are too vague, that could be corrected. However; I feel that folks deserve better than "You either understand it or you don't," as that's what Wikipedia is for.

Regards,

Jonathan JonathanD (talk) 01:31, 11 June 2011 (UTC)

minor revisions to 2nd paragraph
Since I took the liberty to revert and restore the 2nd paragraph, I figured I should also look into why it was deleted. I realize any plain-language description is going to be somewhat imprecise or inadequate, but I since adjusted phrasing and added a caveat to make it more true to fact. Please leave a comment here if what is written in paragraph two appears too vague or misleading, as when I came to this article I did find a 'too technical' tag which asked for an explanation geared to non-experts.

I thought the article was well-written before my contributions, because it well explained why some ideas in Decoherence Theory run counter to the way things are handled in other areas of Quantum Mechanics. However; without paragraph two, it may indeed have been too technical for non-experts to grasp some of those subtleties.

Thanks, JJD JonathanD (talk) 01:47, 12 June 2011 (UTC)

New lead?
I hadn't looked at this article in almost a year, and I do not like the introduction (lead) section. Decoherence is an important enough topic in quantum mechanics that if a lay person who has been reading about QM came across the word, at Wikipedia he or she should be able to find something that can be understood. Providing an external link right there in the lead, for readers unfamiliar with the jargon, is unsatisfactory.

I have an ongoing project where I heavily reorganize and in some cases rewrite sections of articles where it is needed. I recently redid the lead of the Double-slit experiment article; compare the current version to an older version. I'd like to take a crack at re-doing this lead. I will post a draft in my user space and invite comment. In the mean time, if you have any ideas on directions the lead should take, please sound off. Similar to the double-slit article, I feel that technical details belong in the body of the article, and for the lead I will concentrate on providing a clear and readable introduction to the topic. Thanks.  -Jord gette  [talk]  08:00, 27 August 2011 (UTC)

Intro: Unitary link
In "Viewed in isolation, the system's dynamics are non-unitary", the link on "unitary" points to "Unitary operator". Would it be better to instead point to "unitary (physics)"? Gwideman (talk) 09:44, 19 August 2012 (UTC)

Edit 5-22-2013 - math syntax fix correct?
I fixed an error in the math syntax missing brackets following a /mathbf command. I think it's correct.. given that I know absolutely nothing about bra-ket notation nor any of the other notation used.. Is it correct? (and what does the /mathbf command code for anyway?) Jimw338 (talk) 16:18, 22 May 2013 (UTC)
 * If /mathbf doesn't have an immediate bracket, it modifies the next element; in most cases, that is a /mathit followed by a bracket. It's possible that it would be cleaner to replace /mathbf/mathit {{  by  /mathbf{/mathit{ , but it shouldn't be necessary.  (Changing all forward slashes to backslashes, of course.)  — Arthur Rubin  (talk) 17:29, 22 May 2013 (UTC)
 * I guess it is necessary. Oh, well; fixed.  — Arthur Rubin  (talk) 17:33, 22 May 2013 (UTC)

Merge

 * Coherence (physics)

The merge template has been in place since September 2013 and has not generated any discussion that I can find, but it wasn't set up to link to a specific talk section, which I have now done. If no discussion is forthcoming, the ignored merge templates should someday be removed from both articles. &mdash; MaxEnt 10:52, 24 July 2014 (UTC)
 * I am removing them. Decoherence is enough of a distinct concept that it should maintain its own article. PorkHeart (talk) 21:42, 13 October 2014 (UTC)

new first paragraph
This is a suggestion for a new first paragraph. The aim is to make the beginning of the article more accessible to non-experts. Edits are appreciated.

In quantum mechanics, light particles such as electrons behave like waves and are described by a wave function. These waves can interfere, leading to the peculiar behaviour of quantum particles. As long as there exists a definite phase relation between different states, the system is said to be coherent. This coherence is a fundamental property of quantum mechanics, and is necessary for the function of quantum computers. However, when a quantum system is not perfectly isolated, but in contact with its surrounding, the coherence decays with time, a process called quantum decoherence. As a result of this process, the quantum behaviour is lost.

Agdijkstra (talk) 15:20, 16 September 2015 (UTC)

Mistake
you said: "As long as there exists a definite phase relation between different states...", this is metaphysical, not physical. Always (read noise theory) there is relationship and coherence, it simply gets extremely complicated. What you said has nothing to do with Fourier analysis. Major mistakes like that, confuse the students!
 * some systems have a critical threshold of quantum decoherence or extremely complicated coherence, there is no absolute decoherence in nature (except iff one makes a mistake somewhere in the math)
 * the Big Bang was an adiabatic transition of an extremely old, cold, and sparse universe. That is only one example. Understanding quantum coherence and decoherence is way more fundamental and wide than understanding universal mechanics.
 * that part is correct: "A total superposition of the global or universal wavefunction still exists (and remains coherent at the global level)", when maths exist, the non functional interpretations are a mistake. Some interpretations survive under various examples, but not all!!! — Preceding unsigned comment added by 2A02:587:4100:6200:814A:9F79:B36A:6C39 (talk) 11:45, 5 January 2017 (UTC)

Tony Leggett's Nobel talk
"As always, I hear people murmur the dreaded word “decoherence”. But I claim that this is a major red herring". It is curious that critical arguments about decoherence in a Nobel talk do not deserve a mention in the article. Leggett addresses the issue of decoherence also in "Testing the limits of quantum mechanics: motivation, state of play, prospects", Journal of Physics: Condensed Matter, Volume 14, Number 15. I quote: "Let us now try to assess the decoherence argument. Actually, the most economical tactic at this point would be to go directly to the results of the next section, namely that it is experimentally refuted! However, it is interesting to spend a moment enquiring why it was reasonable to anticipate this in advance of the actual experiments. In fact, the argument contains several major loopholes ...". Again, no mention in the WP article. 84.73.134.206 (talk) 11:47, 12 April 2017 (UTC)
 * So fix it. El_C 11:52, 12 April 2017 (UTC)
 * Есть,товарищ комиссар! 84.73.134.206 (talk) 14:23, 12 April 2017 (UTC)

These Leggett quotes are now in the article under "criticisms," but they are completely vague and useless. They need to be supplemented or replaced with an actual *description* of the specific loopholes and experimental evidence referred to. Barring that, the quote should just be removed, it adds nothing by itself.ScottForschler (talk) 14:23, 11 October 2019 (UTC)
 * Came across that section, checked the talk page to see I'm not the only one with the problem, edited the section.Ketarax (talk) 09:48, 4 November 2021 (UTC)

First line
The first line: ''Quantum decoherence is the loss of quantum coherence. In quantum mechanics, particles such as electrons behave like waves and are described by a wavefunction. These waves can interfere, leading to the peculiar behaviour of quantum particles'', seems to imply that the wavefunction of an electron is what causes it to be a wave or describes the wave nature itself when it instead really describes the quantum state of the system with associated probability amplitude. It also seems to suggest that interference of electron waves bring about quantum behaviour when wave nature is a consequence of QM.

I suggest that this be rewritten to: Quantum decoherence is the loss of quantum coherence. In quantum mechanics, particles such as electrons are described by a wavefunction, a mathematical description of the quantum state of a system. It is the probabilistic nature of the wavefunction that gives rise to various quantum effects.

-Harkirat K — Preceding unsigned comment added by Harkirat Kler1 (talk • contribs) 22:28, 21 November 2017 (UTC)

mechanism
As a beginner I find this section confusing. It doesn't seem to actually propose a mechanism for decoherence, and the qualitative description afaict is very vague. It makes an analogy with classical thermodynamics, which postulates a mechanism (say if you pour hot water into cold water) where molecules collide with each other, transferring momentum between molecules until after a while, everything has averaged out. But there's not an analogous explanation of how quantum states get entangled.

Also, it talks about a 6N-dimensional phase space and says "the combined state vector time-evolves a path through the "larger volume", whose dimensionality is the sum of the dimensions of the two subspaces" without saying whether this is just the classical analogy, or if it's also supposed to apply to the quantum system. I was going to edit it to say "classical" but I'm unsure enough that I decided to post here instead. In the quantum case, I think the combined system's space is supposed to be the tensor product of the subsystems' spaces rather than the Cartesian product, so its dimension would be m×n rather than m+n. Similarly the phase space's dimensionality is exponential in the number of particles rather than linear. I don't know if that affects the analogy much.

It would be nice if the section could be made a little more clear about these issues. The high dimensionality is required in quantum computing so it shouldn't be allowed to slip out of sight. Thanks! 173.228.123.166 (talk) 10:20, 11 April 2018 (UTC)

Pure state???
How can anyone write an article on decoherence and not define a pure state?????????? — Preceding unsigned comment added by Koitus~nlwiki (talk • contribs) 16:37, 3 November 2020 (UTC)