EPR States and Bell Correlated States in Algebraic Quantum Field Theory
A mathematical rigorous definition of EPR states has been introduced by Arens and Varadarajan for finite dimensional systems, and extended by Werner to general systems. In the present paper we follow a definition of EPR states due to Werner. Then we show that an EPR state for incommensurable pairs is Bell correlated, and that the set of EPR states for incommensurable pairs is norm dense between two strictly space-like separated regions in algebraic quantum field theory.
KeywordsEPR states Bell correlated states Algebraic quantum field theory
The author is supported by the JSPS KAKENHI, No.23701009 and the John Templeton Foundation Grant ID 35771.
- 2.Baumgärtel, H.: Operator Algebraic Methods in Quantum Field Theory. Akademie Verlag, Berlin (1995) Google Scholar
- 12.Hofer-Szabó, G., Vecsernyés, P.: Bell inequality and common causal explanation in algebraic quantum field theory (2012). arXiv:1204.5708 [quant-ph]
- 21.Werner, R.F.: EPR states for von Neumann algebras (1999). arXiv:quant-ph/9910077