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I see that Ian Durham created quantum channel
Is that a real thing?
Is that a real thing?
I am not into quantum computation. What I can see is that there is a wikipedia article on "quantum channels" which looks like it may have been in the vicinity when the nLab entry here was created.
But I see room for improvement. Also of the Wikipedia entry, for that matter. But I won't spend time on this now...
Ian Durham is asking for help here on MO
I studied these operators in 1991 in relation to multichannel dissipative processes in atomic and nuclear physics. There is nice non-hermitean perturbation theory in terms of matrix of channel operators. Now it is too far away in my fading memory to be able to contribute at the spot. The only thing is that it should not emphasis like a fad from quantum computation as it was extensively used in other parts of physics decades earlier than quantum computation fad.
Does anybody else agree that the beginning paragraph makes no sense?
...
@Urs: I agree.
I object, your honor! This article is a travesty. It's a travesty of a mockery of a sham of a mockery of a travesty of two mockeries of a sham.
Well we can think about it in two ways: An opportunity to uncover some new mathematics by scraping away the dross, or as something to dismiss as mucky. If it can be salvaged, I prefer the former, hence my efforts there. If we have one physicist curious about category theory and willing to try, then perhaps there will be more. Of course, we still have the lesson of one JA in the back of our collective mind - this wiki does have a specific purpose and that is not to be an open book for anyone to write whatever pops into their head.
I claim that Ian does not have a formidable enough grasp of mathematics to be able to write this article coherently. See this discussion on meta.MO.
Harry, thanks for that link, that is illuminating.
I really don't have time to look into this. From Zoran's comment I gathered that in principle the notion of "quantum channel" exists in standard accepted literature and makes sense -- even if the present nLab article on it is in need of serious improvement.
If so then we should try to eventually have a decent blog entry on it, with due comments on the value of the concept.
To the extent, however, that the entry tries to sell doubtful concepts in JA-manner, we should try to remove these, with due discussion to be sure that those who can claim to grasp the issues at hand agree.
Hmm. ok.
It'll work out better then if he doesn't write it on his own :) (Zoran seems to have some familiarity, which may help)
I'll take any further developments on quantum channels with a grain of salt, but do note that there are others on the wiki who like to play around with basic notions, without getting them right the first time. Ian Durham doesn't appear to be about to start adding profuse, pun-laden references out of tone with the lab all over the place, so I vote for letting things grow a bit organically, but with a gentle and firm guiding hand. Think of it as extracting the facts from a reticent child, and helping them to realise where they went wrong. (and don't worry, Harry, I'm not some sort of Buddhist monk. I've been riled on internet forums before and I know it does noone any good, even the poster)
Let us also not bring the debate from meta.MO here.
Yes, so in fact I want to stress that there is absolutely no demand here that contributors make perfect contributions. Of course we all don't, and most of all nLab entries are very imperfect. The whole point of the undertaking here is to build something decent by incremental improvement.
Better a bad entry on an interesting subject than no entry.
Speaking of gentle and firm guiding hands -- too bad Toby hasn't been much heard from recently!
What does JA stand for?
A user who was individualistic to the point of distraction, and rather fixed in their idiosyncratic ideas, in this collaborative enterprise. The nLab does have a statement of purpose (of sorts) on the front page for a purpose. :)
Is it short for "jackass"?
No. But let us leave the matter there.
too bad Toby hasn't been much heard from recently!
Yes, but did you see his annoncement that he would be less active for a while?
Anybody else find this line classic:
"The following is a proof that a quantum channel is a category. The proof actually proves it is a monoid, but the need for it to be a category becomes more clear when we start dealing with these things en masse."?
Harry, as we tried to indicate gently before: rest assured that you are not alone in finding the entry suboptimal.
I have to say, though, that I am not happy with lots of criticism being voiced on the forum about an entry, without the person voicing the criticism taking steps to improve the given entry! This is unconstructive. You are trying to make us do something instead of doing it yourself.
Go to that entry, hit "edit" and fix all the formulations and statements that are broken. When you have done that, come back here and report on what you did. That would be very much appreciated.
Acting on Urs's urging, I have tried to lay down for Ian's benefit some basic precepts in writing articles such as quantum channel. (Despite that heated exchange between Ian and others at MO, he doesn't seem to be completely unreasonable or closed to advice.)
Thanks, Todd, that looks like very good advice.
I am thinking maybe that the best thing to do would be if somebody who knows what people mean by "quantum channel" just puts in the correct definition and the relevant discussion, so that we can move most of what currently fills the entry into a discussion section.
If anyone can point me to an authorative reference on the notion of quantum channels?.
I do not understand Ian Durham defending his viewpoint that quantum channel has to be limite dto information applications, if the notion of multichannel processes in nuclear physics predates this in quantum physics. Especially look for multichannel decay.
Okay, I have now seen the original article that introduces the notion:
Choi, Completely positive linear maps on complex matrices, Linear Algebra and its Applications Volume 10, Issue 3, June 1975, Pages 285-290
This is a readable one.
This states theorems about linear maps between vector spaces of finite dimensional complex matrices. We should start the entry with that and postpone any discussion of the extension of this to more general spaces of operators on Hilbert spaces to later sections.
Thanks, Urs. Before I saw that, I put down more questions and advice for Ian to consider, mentioning for instance that the regulars don't smile upon islands of isolated activity scattered in the nLab (recall JA), and advising to become better acquainted with what others here are doing and fitting in somehow. You in particular have other ways to spend your time!
I wrote a new version of the entry: quantum channel
The previous version is still at the bottom.
by the way:
as far as I can see, the main point that Ian Durham apparently wanted to make, that quantum channels form a category -- a subcategory of Vect if we restrict to systems with finitely many degrees of freedom -- is perfectly valid and a sensible point to make. (It is however also trivially true, there is nothing non-trivial to prove here.)
I see that the standard physics literature doesn't make that point. But I suppose if we asked Bob Coecke about this, he would be well familiar with it and be able to tell us a bigger story.
You're welcome. Coming from a physics background originally, I like to see category theory put to good use in all things quantum, even if my own predilection is hopelessly abstract, so I'm glad some of Coecke's stuff could fill out our physics side of things.
I wrote back to Ian some clarification in a query box.
added to quantum channel references on the description in terms of dagger-categories by Selinger, Coecke and others, kindly provided tonight by ob Coecke himself.
left "algebraic graffiti" on Bob's whiteboard today - something to do with Frobenius algebras and an inappropriate picture...).
I believe I have seen that earlier today...
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