Abstract
The Leggett–Garg (LG) test of macroscopic realism involves a series of dichotomic non-invasive measurements that are used to calculate a function which has a fixed upper bound for a macrorealistic system and a larger upper bound for a quantum system. The quantum upper bound depends on both the details of the measurement and the dimension of the system. Here we present an LG experiment on a three-level quantum system, which produces a larger theoretical quantum upper bound than that of a two-level quantum system. The experiment is carried out in nuclear magnetic resonance and consists of the LG test as well as a test of the ideal assumptions associated with the experiment, such as measurement non-invasiveness. The non-invasive measurements are performed via the modified ideal negative result measurement scheme on a three-level system. Once these assumptions are tested, the violation becomes small, despite the fact that the LG value itself is large. Our results showcase the advantages of using the modified measurement scheme that can reach higher LG values, since these leave a larger margin for violating the inequality in the face of experimental imperfections.
Highlights
Introduction.—The predictions of quantum mechanics regarding microscopic systems do not carry over to macroscopic objects
Of the three fundamental assumptions: (A1) macroscopic realism (MR): the system cannot be in a superposition of the classically observable state, (A2) non-invasive measurability (NIM): It is possible to measure the macroscopic system without disturbing it, and (A3) induction: the future cannot influence the past, only the last is independent of the experimental setup
The Leggett-Garg inequality (LGI) is therefor a test of MR under a set of reasonable assumptions about the system, in particular a version of NIM
Summary
Introduction.—The predictions of quantum mechanics regarding microscopic systems do not carry over to macroscopic objects. Various experimental tests of 2-level LGI have been performed [5,6,7,8,9,10,11,12,13,14,15,16,17], and in [16, 17] ideal negative result measurements (INRMs) were used to perform non-invasive measurements.
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