Quantum generalizations of Bell's inequality
@article{Cirelson1980QuantumGO, title={Quantum generalizations of Bell's inequality}, author={B. S. Cirel'son}, journal={Letters in Mathematical Physics}, year={1980}, volume={4}, pages={93-100} }
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 of instruments located in different space-time regions is also discussed in some detail.
1,157 Citations
Stronger-Than-Quantum Correlations
- Physics
- 1995
After an elementary derivation of Bell's inequality, classical, quantum mechanical, and stronger-than-quantum correlation functions for 2-particle-systems are discussed. Special functions are…
Bell’s inequalities and quantum field theory
- Physics, Mathematics
- 1990
The present state of mathematically rigorous results about Bell’s inequalities in relativistic quantum field theory is reviewed. In addition, the nature of the statistical independence of algebras of…
Quantum analogues of the Bell inequalities. The case of two spatially separated domains
- Mathematics
- 1987
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…
Experimental tests of general quantum theories
- Philosophy
- 1987
Bell-type inequalities can be used to test the general framework not only of classical theories but also of quantum theories. A common algebraic origin of such inequalities is discussed.
Bell's inequality for a single particle
- Physics
- 1996
Bell's inequality must be satisfied by a theory that can be based on local realistic variables. We derive such an inequality and show that it is violated by some quantum mechanical states. These…
Generalizing Tsirelson's bound on Bell inequalities using a min-max principle.
- MathematicsPhysical review letters
- 2004
Bounds on the norm of quantum operators associated with classical Bell-type inequalities can be derived from their maximal eigenvalues. This quantitative method enables detailed predictions of the…
An application of Bell's inequalities to a quantum state extension problem
- Mathematics
- 1989
Using techniques from the study of quantum violations of Bell's inequalities, we give examples of three C*-algebras A, B, C, and states ω12 on A ⊗ B, and ω23 on B ⊗ C, which agree on B, but do not…
Bell's inequality for mixed states
- Physics
- 1992
Violation of Bell's inequality for mixed states is considered. The authors show that a mixture of states that are macroscopically essentially equivalent may suppress the violation. Thus in general…
References
SHOWING 1-6 OF 6 REFERENCES
Bell's theorem. Experimental tests and implications
- Philosophy
- 1978
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 are…
An operational approach to quantum probability
- Mathematics
- 1970
In order to provide a mathmatical framework for the process of making repeated measurements on continuous observables in a statistical system we make a mathematical definition of an instrument, a…
experimental tests and implications', Rep
- Progr. Phys. 41, 12, 1881-1927
- 1978