  In 1985, Leggett and Garg (1985 Phys. Rev. Lett. 54 857) proposed a Bell-like
inequality to test (in)compatibility between two fundamental concepts of
quantum mechanics. The first concept is 'macroscopic realism', which is the
quality of a physical property of a quantum system being independent of
observation at the macroscopic level. The second concept is 'noninvasive
measurability', which is the possibility of performing a measurement without
disturbing the subsequent evolution of a system. One of the key requirement for
testing the violation of the Leggett-Garg inequality, or Bell's time
inequality, is the ability to perform noninvasive measurements over a qubit
state. In this paper, we present a quantum scattering circuit that implements
such a measurement for maximally mixed states. The operation of the circuit is
demonstrated using liquid-state nuclear magnetic resonance (NMR) in chloroform,
in which the time correlations of a qubit are measured on a probe (ancillary)
qubit state. The results clearly show a violation region and are in excellent
agreement with the predictions of quantum mechanics.

Quantum Physics