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Bell Correlated and EPR States in the Framework of Jordan Algebras

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Abstract

We study Bell inequalities and EPR states in the context of Jordan algebras. We show that the set of states violating Bell inequalities across two operator commuting nonmodular Jordan Banach algebras is norm dense in the global state space. It generalizes hitherto known results in quantum field theory in several directions. We propose new Jordan quantity for incommensurable observables in a given state, introduce the concept of EPR state for Jordan structures, and study relationship between EPR states and Bell correlated states. Our analysis shows crucial role of spin factors and Pauli spin matrices for studying noncommutative properties of states and observables.

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Acknowledgments

This work was supported by the “Grant Agency of the Czech Republic”, Grant No. P201/12/0290 “Topological and geometrical properties of Banach spaces and operator algebras”.

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  1. Department of Mathematics, Faculty of Electrical Engineering, Czech Technical University in Prague, Technická 2, 166 27, Praha 6, Czech Republic

    Jan Hamhalter & Veronika Sobotíková

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  1. Jan Hamhalter
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  2. Veronika Sobotíková
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Correspondence to Veronika Sobotíková.

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Hamhalter, J., Sobotíková, V. Bell Correlated and EPR States in the Framework of Jordan Algebras. Found Phys 46, 330–349 (2016). https://doi.org/10.1007/s10701-015-9966-6

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  • DOI: https://doi.org/10.1007/s10701-015-9966-6

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