Causal Emergence in Quantum Mechanics

Causal emergence is brought about when a coarse-grained description of a physical system is more effective (more deterministic and/or less degenerate) than the fine-grained corresponding model. We show, for the first time to our knowledge, a causal emergence in a quantum system: a atomic Mach-Zehnder interferometer with two which-path detectors. The atomic wave-like or particle-like descriptions are related, respectively, to $\mathit{\text{coarse-grained}}$ and $\mathit{\text{fine-grained}}$ models. The predictions of the atomic position after the passage through the interferometer when the to $\mathit{\text{coarse-grained}}$ description is considered are more effective than the corresponding $\mathit{\text{fine-grained}}$ model. We conclude that quantum eraser measurements yields the causal emergence in this system.