Talk:Tsirelson's bound

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1. Thank you for your interesting article on `my bound'.

2. I am astonished by the order `proof - formulation - interpretation'. In journal articles, it is usually `introduction - formulation - proof'. For an encyclopedia it is even more important (so I think), to start with an informal explanation (what is it good for), then give an exact formulation, and then (if at all) a proof.

3. The notion `operator' could be more clear. Many people believe that operator is usually a linear transformation of a Hilbert space (I mean, in the context of quantum theory; in general, the space may be Banach etc, and the operator may be nonlinear). I guess that your notion of operator is sometimes (or always?) different; probably you mean an element of some algebra (associative? ordered? C-star algebra?) or even someting more general (what exactly?). Could you please be more explicit?

4. More than 80 relevant references are collected on my site, here: [1] Maybe, an external link to it would be appropriate.

--Boris Tsirelson

Maybe I shouldn't throw any stones, but it seems to me this article could be much clearer, for instance following the exposition given in Asher Peres' book p 174 which is self-contained and lucid. CSTAR 20:40, 15 Feb 2005 (UTC)

[edit] Proposed change

Suppose

XA,YA,XB,YB

are self-adjoint operators such that

X_A^2= Y_A^2= X_B^2= Y_B^2=1

and the A operators commute with the B operators, that is

[XA,XB] = [XA,YB] = [YA,XB] = [YA,YB] = 0

Then for any state φ,

\langle X_A X_B \rangle_\phi + \langle X_A Y_B \rangle_\phi + \langle Y_A X_B\rangle_\phi - \langle Y_A Y_B \rangle_\phi \leq 2 \sqrt{2}

and the upper bound is achieved by the Pauli spin matrices as in the Bell theorem article. The proof considers

C = XAXB + XAYB + YAXB − YAYB

and computes C2.

This would mean deleting most of what is written in the article currently.CSTAR 06:21, 19 Feb 2005 (UTC)

My knee-jerk reaction is that rewriting in this way would be a good idea. It would also be nice to have a statement of the theorem before launching into its proof. I might give this a shot on some rainy day. linas 22:22, 18 July 2005 (UTC)

Please fix the encoding of the proof starting F • U + F • V + U • G - V • G on the article page, in my browser the bold font renders the minus sign like a smaller dot so that last term looks like U • G • V • G.

[edit] Formatting

Is there a particular reason that the equations and inequalities show up in text form and not in .png form with all the nice and tidy formating?