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arXiv · 2610.23264

Anticommuting Displacement Operators, Exact Pauli Algebras,and the Singlet State from the Oscillator Vacuum

S. P. Sorella
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Abstract

We give an explicit construction of a pair of anticommuting Weyl displacement operators for a harmonic oscillator and use bounded functional calculus to obtain exact dichotomic representatives of the Pauli algebra. Two independent oscillators provide commuting Pauli algebras for Alice and Bob. The standard singlet-sector projector, written entirely in terms of these bounded oscillator observables, is then applied to the two-oscillator vacuum. We show explicitly that the projected vacuum has nonzero norm, so its normalization is well defined, has the exact singlet correlations, and reaches the Tsirelson value $2\sqrt2$ for the usual Bell--CHSH settings. We also clarify that the construction generally realizes a singlet sector with multiplicity, rather than selecting a unique vector in the full oscillator Hilbert space, and we compare the construction with the older pseudospin approach to continuous-variable Bell tests.

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BibTeXRIS

S. P. Sorella. 2026-10-16. Anticommuting Displacement Operators, Exact Pauli Algebras,and the Singlet State from the Oscillator Vacuum. https://arxiv.org/abs/2610.23264

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