Necessary and sufficient conditions for macroscopic realism from quantum mechanics

TL;DR

This paper establishes that a combination of no-signaling in time (NSIT) conditions is both necessary and sufficient for macrorealism, providing a new operational framework for testing classicality in quantum systems.

Contribution

It proves that NSIT conditions fully characterize macrorealism and introduces an operational formulation using POVMs and Hamiltonians for practical tests.

Findings

NSIT conditions are necessary and sufficient for macrorealism

Operational formulation of NSIT with POVMs and Hamiltonians

Application to coarse-grained quantum measurements

Abstract

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 non-classical 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 measurements and the system Hamiltonian. We argue that this leads to a suitable definition of "classical" measurements and Hamiltonians, and apply our formalism to some generic coarse-grained quantum measurements.