Room 117

Recent results on Tsirelson's problem

Manik Banik

IMSc

Tsirelson's problem asks whether the commuting operator model for two-party quantum correlations is equivalent to the tensor-product model. Recently, W. Slofstra reported some breakthrough development in this
direction. He proved the negative answer to the middle Tsirelson's problem and also solved some interesting related problems

I will try to discuss what the Tsirelson's problems mathematically are and what Slofstra has proven recently. I will not go into the detailed proof techniques of Slofstra, rather I will discuss about (binary) linear system games (interesting example: quantum magic game by Mermin-Peres) and how it is related to the Tsirelson's problem. Finally, I will try to make few comments why Slofstra's results are important in quantum foundations.

Related paper(s):

1. R. Cleve and R. Mittal, Characterization of Binary Constraint System
Games, Automata, Languages, and Programming, Lecture Notes in Computer
Science, no. 8572, Springer Berlin Heidelberg, 2014, arXiv:1209.2729,
pp. 320– 331.

2. A. Arkhipov, Extending and Characterizing Quantum Magic Games,
arXiv:1209.3819

3. R. Cleve, L. Liu, and W.Slofstra, Perfect commuting-operator strategies
for linear system games, Journal of Mathematical Physics (2016), to appear (
arXiv:1606.02278).

4. W. Slofstra, Tsirelson's problem and an embedding theorem for groups
arising from non-local games, arXiv: 1606.03140

5. W. Slofstra, The set of quantum correlations is not closed, arXiv:
1703.08618