Talk:No-cloning theorem

Clarification of implications?
This is generally a very clear article, but the principle raises some questions for newcomers. The second paragraph deals with quantum entanglement, but what about Bose–Einstein condensates and lasers? In the case of a condensate, I guess the same quantum state is reached because it is a known and definite state forced by cooling, rather then a superposition. But does a photon in a laser not stimulate emission of another identically-polarised photon, even if that polarisation is not known? --Cedderstk 08:25, 16 May 2006 (UTC)
 * I think that would be an example of entanglement. E.g., if |0> and |1> are the two possible polarization states of the inital photon, then the final state can be |0>|0> or |1>|1>.  So, if we start with a superposition of |0> and |1> (with coefficients a and b), we have:
 * a|0> + b|1> --> a|0>|0> + b|1>|1>
 * Whereas, for cloning we would need:
 * a|0> + b|1> --> (a|0> + b|1>)x(a|0> + b|1>) = aa|0>|0> + ab|0>|1> + ba|1>|0> + bb|0>|0>
 * In other words, cloning refers to the creation of two separable states, and that's what the theorem forbids. -- Tim314 00:37, 19 February 2007 (UTC)

Second law of thermodynamics
Dosnt this rule break the second law of thermodynamics ie A is destroyed in a case of quantum teleportation? — Preceding unsigned comment added by 124.170.0.157 (talk) 13:28, 5 April 2012 (UTC)
 * The state of A becomes |0> or |1>. By destroyed, we mean the state changes to one of these values. Does that address your concern? My knowledge of physics is limited. Skippydo (talk) 14:20, 5 April 2012 (UTC)

No-cloning prevents superluminal communication?
The article states, "The no cloning theorem prevents superluminal communication via quantum entanglement, as cloning is a sufficient condition for such communication." Logically, this makes no sense: to prevent superluminal communication, cloning would have to be a _necessary_ condition. As stated, there is nothing to say that some condition other than cloning might also imply superluminal communication. Indeed, if cloning implies superluminal communication, then a proof of no superluminal communication would imply no-cloning as a corollary.


 * yes, you're right. feel free to modify the article. Mct mht 02:31, 26 June 2007 (UTC)


 * In your contrapositive the consequent is missing a negation. You are correct in stating that the no-cloning theorem is a corollary of no superliminal communication. Skippydo 05:24, 26 July 2007 (UTC)


 * The no cloning theorem indeed prevents superluminal communication via quantum entanglement. Following the thought experiment in that paragraph, no matter Alice perform measurements or not, Bob alway got an ensemble of mixed state. The reason is because if Alice really performs an experiment, Bob will randomly get |+z> or |-z> state, he does not know which state he has, so following no cloning theorem, he can not clone enough states to perform a coherent experiment to see if he really gets a pure state. So at the end overall he only has a bunch of equal mixed states which is equivalent to the situation Alice does not make any measurement. So Bob can not distinguish whether Alice performs an experiment or not. — Preceding unsigned comment added by 128.42.156.137 (talk) 20:21, 1 July 2013 (UTC)


 * Superluminal's got nothing to do with it. You can't communicate sub-luminally, either, that's the no-communication theorem. User:Linas (talk) 21:15, 18 November 2013 (UTC)

Telecloning demonstrated.
There are several articles about telecloning as a fact already made in a laboratory. In arXiv you can find too a lot of topics talking about telecloning. Please, consult this article.

http://www.physorg.com/news10924.html

I'm wondering if could be appropriated, expand the article, talking about telecloning as being also demonstrated in laboratory. I think the article need urgent attention. Is a fact that the no cloning theorem is a topic of phsyics, but is also a fact, that telecloning is being demonstrated, so this article can bring the people to wrong conclussions. It should be expanded, talking about recents experiments in telecloning and quantum mechanics. Thanks.


 * telecloning and cloning are not the same. telecloning is a teleportation-type protocol where shared multipartite entanglement is essential, yet another example of entanglement being the crucial enabler in quantum communication. without shared entanglement: no cloning. the comparison deserves to be mentioned here and some remarks can be added to the teleportation article. but i'd suggest that telecloning be given its own article also. Mct mht 00:23, 26 July 2007 (UTC)


 * To clearify, even with shared entanglement there is no cloning. You may of course teleport an arbitrary state but this will destroy the source leaving only the target qubit. Any article you find about telecloning will no dobt mention the no cloning theorem and state that they will be accepting some error to preform so a called optimal cloning. As always, after reading your link, I must mention that people will never be cloned or teleported using this technique as we are talking about information and not matter. Skippydo 05:17, 26 July 2007 (UTC)


 * Wow, I never expected the article could expand so fast with a part explaining imperfect cloning, I think that it should be expanded a bit more, is very very short. That part added to the article, clarify a lot the things, because cloning telecloning... are similar terms and you get confussed. One thing that have been forgotten is an IMPORTANT POINT, that is the "ACCURACY LEVEL" or... theoretical accuracy level, for imperfect telecloning, which have been demonstrated in a 58%, and is allegedly able to reach a 66%. The accuracy gives us an idea about how well we are doing the copies, I find it interesting to be mentioned


 * Watch this please


 * http://www.nkj.ru/en/news/3775/


 * Someone could add this?

Edit by143.239.130.221, reverted by Mct mht
Is it possible to get an actual reason for the revert as opposed to the "..." that was given? With the exception of a minor typo at one point and some general formatting errors the proof was correct and would be much easier for a layman to "get" since there's no advanced QM formulation like the adjoint present. Hell, my lecturer gave me full credit for using this method in a problem set earlier this year. Also would it kill you to provide actual summaries if you're going to bother to type something in the summary box? Eccentricned (talk) 03:18, 13 May 2008 (UTC)


 * It's certainly as good as the current proof but I oppose it's addition. We only need one version of the proof.


 * I would also, like to point out that the current proof is not sufficiently general. Either axillary qubits need to be added or more general quantum operations need to be allowed. Skippydo (talk) 01:34, 14 May 2008 (UTC)

Article title
Shouldn't the title be No-cloning theorem, as opposed to No cloning theorem? --Robin (talk) 20:02, 5 September 2009 (UTC)


 * It would be great if someone moved this, and the otehr no-xxx articles, from short-dash to long-dash (en-dash to em-dash). I no longer have that ability :-( User:Linas (talk) 21:03, 18 November 2013 (UTC)

Note: the removed and wrong informal proof has been added again!
This old section was removed because it is not only controversial but quite wrong, misleading about the physical consequences of the No-Cloning theorem and also based on a very typical beginner confusion about non-commuting operators, which are pervasive in Quantum Mechanics. Despite of the removal, the old-section has been included again in the "Consequences" sub-section. I really think this article should clarified and re-edited, adding a new section explaining why Cloning does no violate Heisenberg's Uncertainty Principle.

--Garrapito (talk) 15:33, 15 November 2010 (UTC)


 * I think a general section on misconceptions about the theorem could be beneficial, including, as Garrapito suggests, an explanation of the problem with the uncertainty principle argument. A related misconception which could also be addressed is the idea that you can't produce many identical copies of a quantum state.  Of course you can, and in fact this is essential for Quantum State Tomography and other applications; what you can't do is copy an arbitrary, unknown state.  I can try to add such a section when I get a little more free time, unless someone else wants to take a stab at it first. -Tim314 (talk) 16:28, 15 November 2010 (UTC)


 * ====Note: This refers to the subsection titled "Informal Proof", which I have since deleted for the reasons given below====
 * - Note added by Tim314 (talk) 07:03, 15 November 2010 (UTC)

Isn't the informal proof shown misleading? When it says "one could clone particle A's state to particle B, then measure A's position and B's momentum with any desired precision", if he had to measure an eigenstate of the position operator, as position and momentum do not commute, it is impossible to obtain the expected value of the momentum property of the state with arbitrary small uncertainty. The state could be decomposed as a sum of momentum eigenstates, hence, the measurement of p would not be have a well-defined result, no matter how many copies we can make of it. Considering that x and p do not have a common eigenbasis this proof sounds strange to me.

I think that the impossibility of cloning should be compared with the inpossibility of distinguishing non-orthogonal states (as it is done in Nielsen & Chuang). garrapito (talk)
 * Yes the "informal proof" seems quite wrong to me. The reason you can't measure an exact value of momentum and position at the same time is that a quantum mechanical particle doesn't *have* an exact position and an exact momentum at the same time.  Even if you did have two identical copies of a quantum state, if you measure the momentum you are *changing* the state, projecting it into a state with an exact momentum.  And likewise if you measure the position, you are changing the state to one with an exact position.  You're determining the position or momentum *after the change*.  The only way this could be the same as the position and momentum of the initial state is if the particle initially were simultaneously in a state of definite position and a state of definite momentum, and that is impossible.


 * Moreover, there's nothing in the No-Cloning Theorem that forbids you from having two identical copies of a quantum state. It only forbids copying an *arbitrary*, *unknown* quantum state.  So if this argument *were* a legitimate way to violate the uncertainty principle (which it isn't), then it would work just as well without "cloning" (in the sense referred to by the theorem).


 * This "informal proof" is thus more than merely "informal", it is in fact (1) quite wrong, (2) misleading about the nature of the uncertainty principle, and (3) misleading about the nature of the No-Cloning Theorem itself. For this reason, I'm removing it.--Tim314 (talk) 06:55, 15 November 2010 (UTC)

I've removed the offending paragraph. If someone wants to add it, they can provide references for us to verify. Skippydo (talk) 16:19, 17 November 2010 (UTC)


 * I actually tried to look for some references. All the articles I found talking about this problem were, more or less, a copy of the Wikipedia article.


 * Cloning can be shown to be equivalent to the ability of distinguishing non-orthogonal operators. The impossibility of the latter it is indeed related to the Heisenberg principle, but the deleted explanation was wrong. If I have time I will try to write something about this.--Garrapito (talk) 16:31, 19 November 2010 (UTC)

Problems with the formal proof
The formal proof presented in this page is incomplete. One has to prove that no-cloning holds also if one considers an external ancillary system.

In other words, the transformation that has to be proven impossible is


 * psi>|a>|b>  ->   |psi>|psi>|c>

Where the last ket represents an external system initially in a state |a> and finally in the state |c> —Preceding unsigned comment added by 204.121.128.96 (talk) 17:32, 18 June 2010 (UTC)


 * I disagree. Both proofs are equivalent. Given U that clones |psi> in the ancilla system, you can extract from it an unitary operator that works only on the first two qubits that clones the values of the first qubit into the second register. This operator would be  using your notation, where Id is the identity on the first two qubits and x is the tensor product. It is easy to show this operator is unitary and gives the desired effect.


 * You can do it the other way around writing Uancilla = U x |c><b|, which is also unitary and clones. —Preceding unsigned comment added by Garrapito (talk • contribs) 17:15, 19 November 2010 (UTC)

the "example" state vectors
For example:


 * $$ | \phi \rangle = {1 \over \sqrt{2}} \bigg( | 0 \rangle + | 1 \rangle \bigg) $$

and


 * $$ | \psi \rangle = {1 \over \sqrt{2}} \bigg( | 0 \rangle - i| 1 \rangle \bigg) $$

Can someone clarify on what exactly these are examples of? Coz they're neither normalized nor orthogonal to each other.--Dhatsavan (talk) 03:56, 11 January 2011 (UTC)


 * I am not sure, but I think that these (well, their replacement in the present article), are meant to be a demonstration of the particular states which may be cloned. I will attempt to clarify this section, as it confused me as well, even though the theorem is extremely simple.zipz0p (talk) 18:01, 1 August 2011 (UTC)


 * The example is kind-of-bogus; it doesn't really show anything pertinent to the theorem, and mostly serves to confuse and distract the reader. It should probably be removed. User:Linas (talk) 20:54, 18 November 2013 (UTC)

poor wording choices re teleportation
''Similarly, cloning would violate the no-teleportation theorem, which says classical teleportation (not to be confused with entanglement-assisted teleportation) is impossible. In other words, quantum states cannot be measured reliably.

The phrase "classical teleportation" is so misleading is that it should not be spread around these Wikipedia articles beyond the legal minimum.

"Teleportation" is bad enough. Reading through the article on the no-teleportation theorem, either there is no real connection with the notion of teleportation, or the authorsss of the article haven't a clue what the connection is or how to make it plausible.

"Classical teleportation" is much worse. I realize that someone is trying to make a technical distinction here between allowed processes.

But it comes off as referring to some established definition of teleportation according to sober scientific speculative opinion in the classical pre-quantum era. There are a number of counterfactuals here.

My takeaway is that it's quantum jargon that doesn't copy very well, and some of it should simply be left in the original vessels (research papers).

If the field is more than 50% jargon then on the complementarity principle we stand a good chance of capturing 100% of the actually useful part with a single measurement.

(Just to be clear, I'm a big fan of the theory of quantum computing -- as long as it's crisp and clean!) — Preceding unsigned comment added by 178.38.115.176 (talk) 00:11, 5 May 2015 (UTC)


 * Fixed. I just wrote this:
 * Similarly, cloning would violate the no-teleportation theorem, which says that it is impossible to convert a quantum state into a sequence of classical bits (even an infinite sequence of bits), copy those bits to some new location, and recreate a copy of the original quantum state in the new location. This should not be confused with entanglement-assisted teleportation), which does allow a quantum state to be destroyed in one location, and an exact copy to be recreated in another location.
 * I think that solves the problem, right? 67.198.37.16 (talk) 18:57, 23 September 2015 (UTC)

Why so much category theory
Why does this article have so many references to category theory --- and so close to the top of the article! This is really a pretty fringe view of quantum mechanics. Most people working in quantum could lecture for two hours and never mention the word category. I think the average reader is probably more baffled by the references than informed. (Was it inserted by the authors? Probably!) — Preceding unsigned comment added by 163.1.246.246 (talk) 09:59, 22 October 2020 (UTC)

The initial state |e> does not necessary be unknown
I think even one knows the state in system B and erases the information in B, one can still not clone A into B. The argument still holds even one does not require U to apply for any |e> state. Fangzhangmnm (talk) 00:47, 28 June 2021 (UTC)

No-cloning basically trivial
The no cloning thm is basically trivial and does not need any lengthy proof. Any Unitary operators is linear acting on the state vectors If you have U(a psi1 +b psi2) phi, (a b complex constants, psi's and phi are states) then that equals a (U psi1 phi)+ b (U psi2 phi) But the state (a psi1 +b psi2)(a chi1+b chi2) zeta, ie, the originla state plus a clone, is clearly not linear in a, or b. Thus it cannot arise from a unitary transformation. This is no matter what the states psi1, psi2, chi1, chi2, phi, or zeta are. (the dimensionality of total Hilbert space containing chi times zeta must of course have the same dimensionality as phi). Ie, linearity implies no cloning. It also cannot arise from a measurement. The projection operator onto a measurement outcome is also a linear operator. (assuming that the projection operator is independent of a,b. )

This wiki page should be drastically simplified. — Preceding unsigned comment added by 75.155.165.57 (talk) 05:03, 28 January 2022 (UTC)