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.
Highlights
The notion of realism is central to the classical world view
We show that the Leggett-Garg inequality (LGI) and Wigner’s form of the Leggett-Garg inequality (WLGI) measured range of values show a decisive violation of macrorealism and are perfectly compatible with the quantum mechanically predicted ranges, which we estimate taking into account different forms of experimental nonidealities
We show that all the measured no-signaling in time (NSIT) values are within the statistical fluctuations and can be considered as zero with a bound of the order of 10−2; ensuring the validity of the maintenance of noninvasive measurement (NIM) in our experiment
Summary
The notion of realism is central to the classical world view. It assumes that at any instant, irrespective of whether or not measured, a system is definitely in one of the possible states for which all its observable properties have definite values. Suggested a procedure for testing the validity of the concept of realism for single systems in the macroscopic domain [2] For this purpose, they formulated an inequality involving the observable time-separated correlation functions, known as the Leggett-Garg inequality (LGI). The nonidealness in the empirical implementation of negative result measurement can result in the classical disturbance affecting the measured system, thereby contributing to the observed violation of the macrorealist condition being tested This has been referred to as the clumsiness loophole [26]. In the “IBM quantum experience” (IBM QE) study of the extension of such a test for two or more qubits, the NSIT condition per se has been reformulated in terms of an “invasive-measurement bound,” which is estimated in the context of the relevant circuits in the IBM QE This bound takes into account the clumsiness loophole, and its violation is regarded as signifying the violation of “clumsy macrorealism” in such tests [27]
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