User talk:Sabri Al-Safi

non-signaling

I was the one who copied the text from the nonlocality article. I mentioned it was a copy in the edit summary, if this is important to you. But I'm here because of a more interesting subject. I reckon you're pursuing a PhD in nonlocality. So perhaps you could help me with an archaeology project: do you know who first proved that quantum correlations are non-signaling? The founding fathers obviously did not know this, as seen by the concerns exchanged by Schrödinger and Einstein. But currently everybody knows this, so I assume someone did discover it.

Unfortunately the proof is too obvious, so I fear that no one published it; the only reference I know that has it is Pioronio's thesis, but he does not cite any references (and he's too recent to be the originator).

My interest began because I wanted to add this theorem to the quantum entanglement article, but I couldn't find a suitable reference. Thanks! Tercer (talk) 04:30, 6 April 2011 (UTC)[reply]

Hi there! I know it was you that copied the text, I'm not at all bothered. In fact I took it as a compliment.

You're correct, my PhD is involved with nonlocality (esp. generalized probabilistic theories) and that's a very interesting question. I assume you mean the proof that local operations on Alice's qubit do not change the reduced density matrix of Bob's qubit. I've not looked for it before, and after some searching I cannot find the original proof either, although surely the Nielsen & Chuang textbook will contain a proof and perhaps even a reference? I'll have a look at it tomorrow. The earliest real mention I can find is on page 2 of this 1997 paper by Popescu and Rohrlich: http://pm1.bu.edu/~tt/qcl/pdf/popescus19961f6b707f.pdf however it specifically cites a 1980 paper by Ghirardi, Rimini and Weber, that I do not know and cannot find online.

As a side-note, the no-signaling condition is usually stated slightly differently (and more simply) in the various papers that talk about generalized probabilistic theories. I see it really as equivalent to having a meaningful reduced/marginal state on each subsystem. Jon Barrett takes it as a consequence of commutativity of local operations in his paper: http://arxiv.org/abs/quant-ph/0508211

And Giulio Chiribella does something similar more recently: http://arxiv.org/abs/1011.6451

Good luck with your search, and let me know if you find the treasure! --Sabri Al-Safi (talk) 20:23, 6 April 2011 (UTC)[reply]

I just realised that P & R's seminal "Quantum Nonlocality as an Axiom" paper already talks about quantum theory satisfying relativistic causality, though again I'll wait until I'm in my office to check further.

Also, I'm not sure what you say about Einstein and Schrödinger's concern is correct. I think they would be concerned even if they knew about non-signalling. Einstein's problem with the Copenhagen interpretation was that it predicted a change in the physics at location B, due to actions at location A. This is true regardless of non-signalling; most people think that Einstein's fears about local causality were well-founded, but that his hopes of saving it were not. --Sabri Al-Safi (talk) 20:53, 6 April 2011 (UTC)[reply]

I found the paper P & R cited here. My institution does not gives me access to Springer, but by the abstract I guess this is it. It is also reference 8 of this other paper by P & R. Interestingly, the earlier version of this paper does not contain the reference, so I guess they did the same archaeology job. Thank you very much!

Also, I combed through Nielsen & Chuang, and didn't found even the statement of the theorem.

I did not understand what you mean by a change in the "physics" at location B due to action in A. In what way this could be non-signalling? The whole point of the no-signalling theorem is to say that nothing happens in location B due to action in A. I think they were concerned about signalling regardless of counter-factual definiteness. Well, QM is obviously not Lorenz-invariant, so they knew no reason a priori it should be non-signalling. What else could Einstein consider "spooky action at a distance"? Also, see this book about Schrödinger's concerns. Tercer (talk) 01:41, 7 April 2011 (UTC)[reply]

Einstein must have realised that EPR correlations alone cannot be used to signal information, yet he still used them as a primary example, so I think signalling was not the main premise of his concern. What I mean by "the physics at B" is this: if we believe in Copenhagen, then the physical description of Bob's state changes due to Alice's measurement. We can't use this change to send instantaneous information, however the collapse does occur, and so without doubt the Copenhagen interpretation is inherently a non-local theory. The point of Bell's Theorem was not to show that the Copenhagen interpretation is non-local, but that any reformulation of quantum theory which predicts the same outcomes, must be non-local. I suppose the subtlety lies in the difference between simply talking about measurement outcomes, and regarding the Copenhagen interpretation as a description of Nature.

Does that make sense? Please tell me if I'm babbling like a fool, because I'm still trying to get a grip on this myself. Also, well done finding the Ghirardi et al paper. I had a look through and it does seem to be exactly what you're looking for. --Sabri Al-Safi (talk) 11:47, 7 April 2011 (UTC)[reply]

The problem about interpretations is that everyone has a different view of what the interpretation actually says. My view, that I usually think corresponds to Copenhagen, is that the state is completely subjective, and thus the collapse is just a mathematical artefact of updating the probabilities. Let me explain: if you don't do any change of basis, the collapse of the singlet is as mysterious as the collapse of the (unnormalised) mixed state

|01\rangle \langle 01|+|10\rangle \langle 10|

, that has only classical correlation. It was I who wrote (based on a book) the concept section of the quantum entanglement article, that says pretty much the same thing. Before Alice's measurement, Bob's state is described by p(0) = 1/2, p(1)=1/2, p(0|1) = 1, p(1|0), p(0|0) = 0 and p(1|1) = 0. After is just (for example) p(0) = 1 and p(1) = 0. But the only thing I did is to apply the conditional probabilities. I don't think anyone believe in this collapse of the classical state.

The thing is, for me the Copenhagen interpretation is that you must only talk about measurement outcomes.

The point of Bell's theorem. Well, it's complicated to talk about such subjective stuff. But yes, I agree it's not dependent on interpretation, but it only says the correlations are non-local; it does not say anything about the process by which the non-local correlations are generated. Tercer (talk) 17:35, 7 April 2011 (UTC)[reply]

Yes I see where you're coming from; this is what I guess is called an operational view of quantum mechanics, and it's certainly the language people use in these generalized probabilistic theories. The next question is whether you think this is enough for a complete and satisfactory description of Nature? If you think that the Copenhagen formulation is just a nice way of calculating probabilities, a good question is whether this is representative of a deeper structure. Bell seemed to think so, and Bohmian mechanics heads in that direction (as I understand it). However, some people think that Copenhagen, or many-worlds, is really what is going on in nature - in this case one needs to justify collapse or branch statistics respectively. Of course, there are still more approaches like objective collapse theory and it's very messy, so for now I think it's sensible to stick with operationalist formalism and avoid commitment.

Going back to Bell's Theorem, people even say that many-worlds satisfies locality, by avoiding counterfactual definitess (or realism, perhaps). I have yet to form any strong opinion on that... mostly because the terms used have variable meanings. However, I suppose any "typical" branch will almost always contain sets of measurement outcomes that appear non-local, i.e. violate LHV predictions. --Sabri Al-Safi (talk) 11:53, 8 April 2011 (UTC)[reply]

Complete? Surely. Satisfactory? Too imprecise to argue. In this point I think Bell was making a fool of himself and I side with Bohr and Mermin; at least what I think Bohr thought. Mermin is a lot clearer. I recommend this paper of his. This position I take from a deep belief that Nature is simple. And any proposal to alter standard QM ends up leaving a much more complicated theory, either mathematically (Bohmiam mechanics) or conceptually (many-worlds).

Also, I like very much this quote by Wittgenstein: "What can be said at all can be said clearly, and what we cannot talk about we must pass over in silence.". In the context of QM, I interpret it to mean that what can't be measured does not exist; it makes no sense to talk about the simultaneous value of incompatible measurements; either in the sense of Einstein's elements of reality or a less naïve nonlocal-hidden-variables. Tercer (talk) 18:32, 10 April 2011 (UTC)[reply]

Thank you very much for the Mermin reference, I'll have a read through it when I can. I'm amused that very few people are confident they know what Bohr thought! It's almost like he was playing with us.

I'm interested in what you say about believing Nature to be simple. Is this a belief built up inductively from finding such a claim to be true in many cases? Or is it more like a faith, akin to Einstein's own objective realism? Personally, I'm not convinced that simplicity is anything other than a human/anthropic judgment, so it would take a lot of convincing that Nature should necessarily be so. --Sabri Al-Safi (talk) 14:25, 12 April 2011 (UTC)[reply]

Lol I think Bohr was smart enough to know he was being unclear. Maybe he just couldn't help it. He wasn't really very trollish.

About simplicity, it doesn't have a good justification, that's why I call it a belief. But of course it has origins. Have you noticed, when you were doing some calculations, and somewhere you made a mistake, and the calculations became more and more complicated, to the point of you giving up? Also, when a theory is being develop, there are plenty of mistakes and inconsistencies, and the theory is very difficult. But when it finally arrives it is a lot simpler than its beginnings; a familiar example is quantum mechanics, other is Maxwell's unification of electricity and magnetism. A third reason, that I state tong-in-cheekily, is that if some aspect of Nature is inherently hard and complicated, we will never be able to understand it anyway, so why bother?

And what about you? Do you favour an interpretation of QM? You seem to be a many-worlds kind of guy. Tercer (talk) 04:31, 13 April 2011 (UTC)[reply]

I wouldn't say I favour any interpretation in particular, but I'm happy to have a good old debate on them! When I first understood many-worlds I enjoyed the insight it gave into the measurement process, but it does beg the question of why we only see one "branch" with certain probability. I also like the way Bohmian mechanics retains a kind of definite realism, but again there are problems with explaining the initial distribution. Really I prefer an operationalist view for now but with an open mind to new interpretations or improvements on the old.

There is another thing about simplicity though, going back to what I said about it being anthropic. The same can be said about what is "intuitive" - really it comes down to one's experience and familiarity with certain things, and that can be built up over time. Simple things like counting arguments may have appeared very sophisticated to earlier generations, and they would not agree on the simplicity until being shown the validity step-by-step and then working to internalise it. Many concepts have been refined over tiem to a simpler form, but they still require some degree of internalisation. I should revise what I previously said, that although Nature has no reason to be simple to us, our description of it will invariably become refined into a form where it can be internalised and seen as simple. --Sabri Al-Safi (talk) 15:20, 13 April 2011 (UTC)[reply]

At first I was in love with many-worlds. But then I realised that the technique of entangling the measurement apparatus is just the Church of the Larger Hilbert Space, with no need for interpretation. So I became an interpretation agnostic and a priest of the Church ;p Tercer (talk) 18:09, 14 April 2011 (UTC)[reply]

Sand

A local strategy acheiving $S_{CHSH}$ = 2
	$A_{0}$	$A_{1}$	$B_{0}$	$B_{1}$
a	1	-1
b			1	1

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