## B. Tsirelson | ## Bell inequalities and operator algebras | ## noted failures |

My ideas about quantum Bell-type inequalities, published first in 1980, were scantily noted in 1980-1989 (only by L.Landau, S.Summers, R.Werner and A.Grib, and only the simplest case). Being discouraged, I published in 1993 a survey, without proofs, and quitted. One of the claims in that survey drew attention in 2006, and I was asked by A.Acin for the proof. To my crying shame, my would-be-proof failed badly. Trying to provide a kind of antidote against my toxic claim, I issued in 2006 the question, whether it is true or false, to the now discontinued Braunschweig website on open problems in quantum information theory (see archived copy, see also the first 29 problems in the arXiv; my one was problem 33). I was not the first to ask this question, but probably the first to publish it (my text - pdf), and now it is called "Tsirelson's problem" (rather than "Tsirelson's error").

Some stuff in Quantum Information Theory (QI) is actually interesting. Moreover, in QI there are tons of problems and really cool names for them. Seriously, we will discuss in which sense Tsirelson's conjecture is indeed equivalent to Connes' embedding problem. No wonder, they had a hard time to solve the problem numerically!

(M. Junge, a talk on GPOTS2011, May 2011, Arizona, from the abstract.)

- 2007 M. Navascues, S. Pironio, A. Acin,
"Bounding the set of quantum correlations."
Phys. Rev. Lett.
**98**, 010401. Also arXiv:quant-ph/0607119.) - 2008 M. Navascues, S. Pironio, A. Acin,
"A convergent hierarchy of semidefinite programs characterizing the set of
quantum correlations."
New J. Phys.
**10**, 073013. (Also arXiv:0803.4290.) - 2008 V.B. Scholz, R.F. Werner, "Tsirelson's problem." arXiv:0812.4305.
- 2010 M. Junge, M. Navascues, C. Palazuelos, D. Perez-Garcia, V.B. Scholz, R.F. Werner,
"Connes' embedding problem and Tsirelson's problem."
J. Math. Phys.
**52**, 012102. (Also arXiv:1008.1142.) - 2010 T. Fritz, "Tsirelson's problem and Kirchberg's conjecture." arXiv:1008.1168.
- 2011 N. Navascues, T. Cooney, D. Perez-Garcia, N. Villanueva, "A physical approach to Tsirelson's problem." arXiv:1105.3373.

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