Measuring incompatible observables on entangled states through weak measurements: from single pair measurement of CHSH to testing relativistic independence

Measuring incompatible observables on entangled states through weak measurements: from single pair measurement of CHSH to testing relativistic independence. F.Piacentini, A.Avella, E.Rebufello, S. Virzì, I.P.Degiovanni, M.Gramegna, M.Genovese We present the first single-pair Bell inequality test [1] able to obtain a Bell parameter value for every entangled pair detected. This is made possible by exploiting sequential weak measurements, allowing to perform non-commuting measurements in sequence on the same state, on each entangled particle. Such a feature removes the need to choose between different measurement bases [2]. 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 the wave function collapse and allowing us to exploit this quantum resource for further protocols. Finally, as a further use of sequential weak measurement, we present a test [3] of the relativistic independence. [1] S.Virzì, et al. Quant.Sci. Tech. 9 045027 (2024) [2] M.Genovese & F.Piacentini, arXiv:2409.02510 [3] F.Atzori rt al., PRX quantum 5, 040351 (2024)