Abstract
We point out that, when the dimension of the Hilbert space is greater than two, Bell’s operators entering the Bell-CHSH inequality do exhibit inequivalent unitary matrix representations. Although the Bell-CHSH inequality turns out to be violated, the size of the violation is different for different representations, the maximum violation being given by Tsirelson’s bound. The feature relies on a pairing mechanism between the modes of the Hilbert space of the system.
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Acknowledgements
The authors would like to thank the Brazilian agencies CNPq and FAPERJ for financial support. S.P. Sorella is a level 1 CNPq researcher under the contract 301030/2019–7.
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Sorella, S.P. On the Representations of Bell’s Operators in Quantum Mechanics. Found Phys 53, 59 (2023). https://doi.org/10.1007/s10701-023-00699-6
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DOI: https://doi.org/10.1007/s10701-023-00699-6