Observer Bandwidth and Frequency-Tagged Two-Path Interference: A Thought Experiment in Standard Quantum Mechanics

This is a self-contained thought experiment and short theoretical note within standard quantum mechanics. It analyzes a two-path interferometer (double-slit / Mach–Zehnder) where each path is tagged with a small frequency shift. The paper shows that the unconditional interference visibility is governed by the overlap of the frequency-tag states: when the detector is effectively frequency-blind (coarse-grained), interference is recovered, while frequency-resolving detection makes which-path information accessible and suppresses interference. It also derives the corresponding optimal which-path distinguishability via the Helstrom bound and shows saturation of the standard complementarity relation in the ideal pure-state case. No new dynamics or nonstandard assumptions are introduced; the effect is explained entirely through unitary tagging and measurement resolution.