Necessary and sufficient conditions for macroscopic realism from quantum mechanics

Macroscopic realism, the classical world view that macroscopic objects exist independently of and are not influenced by measurements, is usually tested using Leggett-Garg inequalities. Recently, another necessary condition called no-signaling in time (NSIT) has been proposed as a witness for nonclassical behavior. In this paper, we show that a combination of NSIT conditions is not only necessary but also sufficient for a macrorealistic description of a physical system. Any violation of macroscopic realism must therefore be witnessed by a suitable NSIT condition. Subsequently, we derive an operational formulation for NSIT in terms of positive operator-valued measures and the system Hamiltonian. We argue that this leads to a suitable definition of classical measurements and Hamiltonians, and we apply our formalism to some generic coarse-grained quantum measurements.