Single-pair measurement of the Bell parameter

Bell inequalities are one of the cornerstones of quantum foundations, and fundamental tools for quantum technologies. Recently, the scientific community worldwide has put a lot of effort towards them, which culminated with loophole-free experiments. Nonetheless, none of the experimental tests so far was able to extract information on the full inequality from each entangled pair, since the wave function collapse forbids performing, on the same quantum state, all the measurements needed for evaluating the entire Bell parameter. We present here the first single-pair Bell inequality test, able to obtain a Bell parameter value for every entangled pair detected. This is made possible by exploiting sequential weak measurements, allowing to measure non-commuting observables in sequence on the same state, on each entangled particle. Such an approach not only grants unprecedented measurement capability, but also removes the need to choose between different measurement bases, intrinsically eliminating the freedom-of-choice loophole and stretching the concept of counterfactual-definiteness (since it allows measuring in the otherwise not-chosen bases). We also demonstrate how, after the Bell parameter measurement, the pair under test still presents a noteworthy amount of entanglement, providing evidence of the absence of (complete) wave function collapse and allowing to exploit this quantum resource for further protocols.
Comment: 14 pages, 3 figures