Operational meaning of mode-entanglement Bell violation for neutrinos

Determine whether the Clauser–Horne–Shimony–Holt violation implied by the single-particle-sector expression for the Bell parameter is operationally meaningful for neutrinos, taking into account mode entanglement and superselection constraints.

Background

For the single-occupancy two-qubit state, the paper obtains a Bell parameter satisfying Bmax⁡=21+C2B_{\max}=2\sqrt{1+\mathcal{C}^{2}}, which formally implies a CHSH violation whenever the concurrence is nonzero. The authors caution that the perfect anticorrelation in the occupation sector and the associated measurements involve superpositions of different occupation numbers of a single mode.

Consequently, the formal Bell violation may not directly correspond to an operationally realizable neutrino nonlocality test. Its physical interpretation requires resolving the relationship between mode entanglement, allowed measurements, and superselection rules.

References

Taken at face value this implies a Clauser--Horne--Shimony--Holt violation for any $\mathcal{C}>0$. The $T_{zz}=-1$ responsible for it reflects the single-particle sector, in which exactly one flavor mode is occupied, so the measurements involved superpose different occupation numbers of a single mode. Whether that is operationally meaningful for neutrinos raises questions of mode entanglement and superselection that we do not address; $B_{\max}$ is used here only as an example of a quantifier with an analytic response.

— Response of Hellinger-distance based coherence to weak decoherence in two-flavor neutrino oscillations  (2609.27697 - Rai et al., 23 Sep 2026) in Footnote to Section A, Appendix B (Other quantifiers for this state family)