How much quantum weirdness does the quantum switch actually need?

The quantum switch lets operations happen in a superposition of causal orders, but how much quantum coherence does that actually require? Systematically destroying quantum information (dephasing) in each part of the process, the authors find a sharp threshold: only when every system is dephased, or only the final output is left coherent, does the exotic causal structure collapse into something classically explainable. A single coherent system anywhere else in the circuit is enough to preserve causal indefiniteness, pinpointing exactly where the nonclassicality lives.