On the representations of Bell's operators in Quantum Mechanics

• URL: http://arxiv.org/abs/2304.05696v3
• Date: Thu, 25 May 2023 11:58:44 GMT
• Title: On the representations of Bell's operators in Quantum Mechanics
• Authors: Silvio Paolo Sorella
• Abstract summary: We show that when the dimension of the Hilbert space is greater than two, Bell's operators exhibit unitarily inequivalent representations. The feature relies on a pairing mechanism between the modes of the Hilbert space of the system.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We point out that, when the dimension of the Hilbert space is greater than two, Bell's operators entering the Bell-CHSH inequality exhibit unitarily inequivalent 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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