Loophole-Free Interferometric Test of Macrorealism Using Heralded Single Photons

We show unambiguous violations of the different macrorealist inequalities, like the Leggett-Garg inequality (LGI) and its variant called Wigner’s form of the Leggett-Garg inequality (WLGI) using a heralded, single-photon-based experimental setup comprising a Mach-Zehnder interferometer followed by a displaced Sagnac interferometer. In our experiment, negative result measurements are implemented as control experiments, in order to validate the presumption of noninvasive measurability used in defining the notion of macrorealism. Among the experiments to date testing macrorealism, the present experiment stands out in comprehensively addressing the relevant loopholes. The clumsiness loophole is addressed through the precision testing of any classical or macrorealist invasiveness involved in the implementation of negative result measurements. This is done by suitably choosing the experimental parameters so that the quantum mechanically predicted validity of the relevant two-time no-signaling in time (NSIT) conditions is maintained in the three pairwise experiments performed to show the violation of LGI or WLGI. Furthermore, importantly, the detection efficiency loophole is addressed in our experimental scheme by adopting suitable modifications in the measurement strategy, enabling the demonstration of the violation of LGI or WLGI for any nonzero 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 a LGI violation of 1.32±0.04 and a WLGI violation of 0.10±0.02 in our setup, where the magnitudes of violation are respectively 8 times and 5 times the corresponding error values, while agreeing perfectly with the ranges of quantum mechanically predicted values of the LGI and WLGI expressions that we estimate by taking into account the nonidealities of the actual experiment. At the same time, consistent with quantum mechanical predictions, the experimentally observed probabilities satisfy the two-time NSIT conditions up to the order of 10^{−2}. Thus, the noninvasiveness in our implemented negative result measurement is convincingly upper bounded to 10^{−2}.