Polynomial Bell Inequalities

被引:120
作者
Chaves, Rafael [1 ,2 ,3 ]
机构
[1] Univ Freiburg, Inst Phys, D-79104 Freiburg, Germany
[2] Univ Freiburg, FDM, D-79104 Freiburg, Germany
[3] Univ Cologne, Inst Theoret Phys, D-50937 Cologne, Germany
关键词
QUANTUM; NONLOCALITY; GEOMETRY;
D O I
10.1103/PhysRevLett.116.010402
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
It is a recent realization that many of the concepts and tools of causal discovery in machine learning are highly relevant to problems in quantum information, in particular quantum nonlocality. The crucial ingredient in the connection between both fields is the mathematical theory of causality, allowing for the representation of arbitrary causal structures and providing a rigorous tool to reason about probabilistic causation. Indeed, Bell's theorem concerns a very particular kind of causal structure and Bell inequalities are a special case of linear constraints following from such models. It is thus natural to look for generalizations involving more complex Bell scenarios. The problem, however, relies on the fact that such generalized scenarios are characterized by polynomial Bell inequalities and no current method is available to derive them beyond very simple cases. In this work, we make a significant step in that direction, providing a new, general, and conceptually clear method for the derivation of polynomial Bell inequalities in a wide class of scenarios. We also show how our construction can be used to allow for relaxations of causal constraints and naturally gives rise to a notion of nonsignaling in generalized Bell networks.
引用
收藏
页数:6
相关论文
共 67 条
[1]   Device-independent security of quantum cryptography against collective attacks [J].
Acin, Antonio ;
Brunner, Nicolas ;
Gisin, Nicolas ;
Massar, Serge ;
Pironio, Stefano ;
Scarani, Valerio .
PHYSICAL REVIEW LETTERS, 2007, 98 (23)
[2]   Entanglement percolation in quantum networks [J].
Acin, Antonio ;
Cirac, J. Ignacio ;
Lewenstein, Maciej .
NATURE PHYSICS, 2007, 3 (04) :256-259
[3]  
[Anonymous], 1999, UNC ART INT P
[4]  
[Anonymous], 2009, CONVEX OPTIMIZATION
[5]  
[Anonymous], 2001, Causation, Prediction, and Search
[6]  
[Anonymous], 1989, LECT NOTES PHYS
[7]   Nonlocal correlations as an information-theoretic resource [J].
Barrett, J ;
Linden, N ;
Massar, S ;
Pironio, S ;
Popescu, S ;
Roberts, D .
PHYSICAL REVIEW A, 2005, 71 (02)
[8]  
Bell J. S., 1964, Physics Physique Fizika, V1, P195, DOI [DOI 10.1103/PHYSICSPHYSIQUEFIZIKA.1.195, 10.1103/Physics-PhysiqueFizika.1.195]
[9]   Robust nonlocality tests with displacement-based measurements [J].
Bohr Brask, Jonatan ;
Chaves, Rafael .
PHYSICAL REVIEW A, 2012, 86 (01)
[10]  
Bonet B., 2001, P 17 C UNC ART INT A, P48