Loophole free interferometric test of macrorealism using heralded single photons

Abstract: We show unambiguous violations of different macrorealist inequalities, like the LGI and the WLGI using a heralded, single-photon based experimental setup comprising one Mach-Zehnder interferometer followed by a displaced Sagnac one. The negative result measurements (NRM) are implemented in order to validate the presumption of non-invasive measurability used in defining macrorealism. Among all the experiments to date testing macrorealism, the present experiment stands out in comprehensively addressing the relevant loopholes. The clumsiness loophole is addressed through precision testing of any classical invasiveness involved in the implementation of NRMs. This is done by suitably choosing the experimental parameters so that the quantum mechanically (QM) predicted validity of all the relevant two-time no-signalling in time (NSIT) conditions is maintained in all the three pairwise experiments performed to show LGI/WLGI violation. Further, importantly, the detection efficiency loophole is addressed by adopting suitable modifications in the measurement strategy enabling the demonstration of the violation of LGI/WLGI for any non-zero detection efficiency. We also show how other relevant loopholes like the multiphoton emission loophole, coincidence loophole, and the preparation state loophole are all closed in the present experiment. We report the LGI violation of $1.32 \pm 0.04$ and the WLGI violation of $0.10 \pm 0.02$, where the magnitudes of violation are respectively 8 times and 5 times the corresponding error values, while agreeing perfectly with the ranges of the QM predicted values of the LGI, WLGI expressions that we estimate by taking into account the non-idealities of the actual experiment. Simultaneously, the experimentally observed probabilities satisfy all the two-time NSIT conditions up to the order of $10^{-2}$, which ensures non-invasiveness in the implemented NRMs.