Quantum analogues of the Bell inequalities. The case of two spatially separated domains

@article{Tsirelson1987QuantumAO,
  title={Quantum analogues of the Bell inequalities. The case of two spatially separated domains},
  author={B. Tsirelson},
  journal={Journal of Soviet Mathematics},
  year={1987},
  volume={36},
  pages={557-570}
}
  • B. Tsirelson
  • Published 1987
  • Mathematics
  • Journal of Soviet Mathematics
One Investigates inequalities for the probabilities and mathematical expectations which follow from the postulates of the local quantum theory. It turns out that the relation between the quantum and the classical correlation matrices is expressed] in terms of Grothendieck's known constant. It is also shown that the extremal quantum correlations characterize the Clifford algebra (i.e., canonical anticommutative relations). 
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References

SHOWING 1-7 OF 7 REFERENCES
Quantum generalizations of Bell's inequality
Even though quantum correlations violate Bell's inequality, they satisfy weaker inequalities of a similar type. Some particular inequalities of this kind are proved here. The more general case ofExpand
Bell's inequalities and experimental verification of quantum correlations at macroscopic distances
In recent years the fulfillment of the inequalities established by Bell has been tested in different laboratories in the world. These inequalities make it possible to establish which of theExpand
Bell's theorem. Experimental tests and implications
Bell's theorem represents a significant advance in understanding the conceptual foundations of quantum mechanics. The theorem shows that essentially all local theories of natural phenomena that areExpand
Elements of the theory of representations
First Part. Preliminary Facts.- 1. Sets, Categories, Topology.- 1.1. Sets.- 1.2. Categories and Functors.- 1.3. The Elements of Topology.- 2. Groups and Homogeneous Spaces.- 2.1. TransformationExpand
Constructive generalization of Bell’s inequalities
SummaryA process to construct all generalizations of Bell’s inequalities in a given experimental situation is presented. In view of the completeness thus obtained, we address a criticism to a veryExpand
Constantes de Grothendieck et fonctions de type positif sur les sphères
SoitL un espace de Banach reticule (“Banach lattice”) sur R. Si x1 ,..., xk EL on definit (x1” + ..’ + Xk2)1/2 = sup(‘ylxl + ... + c+& ; OLr ,..., CQ E R, a12 + ... + 01~~ = 1) (cette borneExpand