Interference experiment, anomalous weak value and Leggett-Garg test of macrorealism

Macrorealism is a classical world view asserting that the properties of macro-objects exist independently and irrespective of observation. One practical approach to test this view in quantum theory is to observe the quantum coherence for macro-object in an interference experiment. An elegant and conceptually appealing approach for testing the notion of macrorealism in quantum theory is through the violation of Leggett-Garg inequality. However, a conclusive Leggett-Garg test hinges on how the non-invasive measurability criteria is guaranteed in an experiment and remains a debated issue till date. In this work, we connect the practical and the conceptual approaches for testing the macrorealism through the weak value. We argue that whenever quantum effect is observed in an interference experiment there is an existence of anomalous weak value. Further, we demonstrate that whenever such weak value exists, one obtains the violation of a Leggett-Garg inequality in any interference experiment. Since the system itself serves as apparatus in a path-only interference experiment, one cannot salvage the macrorealism by abandoning the non-invasive measurability assumption. We provide a rigorous discussion about the assumptions involved in Leggett-Garg scenario and how our scheme fits into it. Further, using the quasiprobability approach we explain how non-invasive measurability condition is satisfied in our scheme.