Extremal Tsirelson inequalities (2401.12791v2)
Abstract: It is well-known that the set of statistics that can be observed in a Bell-type experiment is limited by quantum theory. Unfortunately, tools are missing to identify the precise boundary of this set. Here, we propose to study the set of quantum statistics from a dual perspective. By considering all Bell expressions saturated by a given realization, we show that the CHSH expression can be decomposed in terms of extremal Tsirelson inequalities that we identify. This brings novel insight into the geometry of the quantum set in the (2,2,2) scenario. Furthermore, this allows us to identify all the Bell expressions that are able to self-test the Tsirelson realization.
- L. Hardy, Physical Review Letters 71, 1665 (1993).
- D. Mayers and A. Yao, Self testing quantum apparatus (2004), arxiv:quant-ph/0307205 .
- M. Navascués, S. Pironio, and A. Acín, Physical Review Letters 98, 010401 (2007).
- M. Navascués, S. Pironio, and A. Acín, New Journal of Physics 10, 073013 (2008).
- L. Masanes, Necessary and sufficient condition for quantum-generated correlations (2003), arxiv:quant-ph/0309137 .
- S. Ishizaka, Physical Review A 97, 050102 (2018).
- A. Mikos-Nuszkiewicz and J. Kaniewski, Extremal points of the quantum set in the chsh scenario: conjectured analytical solution (2023), arXiv:2302.10658 [quant-ph] .
- B. S. Tsirel’son, Journal of Soviet Mathematics 36, 557 (1987).
- S. Wehner, Phys. Rev. A 73, 022110 (2006).
- N. Miguel and W. Harald, Proc. R. Soc. A 466, 881–890 (2010).
- I. Šupić and J. Bowles, Quantum 4, 337 (2020).
- T. Fritz, Journal of Mathematical Physics 53, 072202 (2012).
- L. J. Landau, Foundations of Physics 18, 449 (1988).
- V. Barizien, P. Sekatski, and J.-D. Bancal, Custom bell inequalities from formal sums of squares (2023), arXiv:2308.08601 [quant-ph] .
- L. Wooltorton, P. Brown, and R. Colbeck, Device-independent quantum key distribution with arbitrarily small nonlocality (2023), arXiv:2309.09650 [quant-ph] .
- W. Slofstra, Forum of Mathematics, Pi 7, e1 (2019).
- D. Collins and N. Gisin, Journal of Physics A: Mathematical and General 37, 1775 (2004).
- B. S. Cirel’son, Letters in Mathematical Physics 4, 93 (1980).
- K. F. Pál, T. Vértesi, and M. Navascués, Phys. Rev. A 90, 042340 (2014).
- M. Ioannou and D. Rosset, Noncommutative polynomial optimization under symmetry (2022), arXiv:2112.10803 [quant-ph] .
- Y.-C. Liang and A. C. Doherty, Phys. Rev. A 75, 042103 (2007).
- C. Bamps and S. Pironio, Physical Review A 91, 10.1103/physreva.91.052111 (2015).
- R. T. Rockafellar, Convex Analysis (Princeton University Press, 1970).
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.