Consequences of the single-pair measurement of the Bell parameter

Abstract: Bell inequalities represent a milestone for contemporary Physics, both for quantum foundations investigation and technological applications (e.g., quantum communication and entanglement certification). Although loophole-free tests have been recently performed, a strong debate is still ongoing on the actual meaning of Bell inequality tests, for example on the possible additional hypotheses (end eventual loopholes) to be included in Bell's theorem, as well as on the implications for certain interpretations of quantum mechanics. A recent work [S. Virz`i et al., Quantum Sci. Technol. 9, 045027 (2024)] challenges some of the statements appeared in this debate, achieving for the first time an experimental estimation of the entire Bell-CHSH parameter from a single entangled pair thanks to a weak-interaction-based measurement approach. Here we analyse the implications of this result for quantum mechanics foundations investigation, illustrating how it can tackle some of the aforementioned interpretations of Bell inequality tests and, more in general, of quantum mechanics itself.