Path-Distinguishability Gaps at Fixed Visibility in Noisy Qubit Interferometers

arXiv:2610.33632v1 Announce Type: new Abstract: The wave--particle duality relation bounds visibility and path distinguishability but does not determine their attainable values in a fixed noisy interferometer. We characterize the complete attainable region for a two-path interferometer with a qubit marker, varying the marker input while fixing the source, preparation channel, path-dependent interaction, and subsequent marker channel. At each feasible fringe visibility, the Helstrom-optimal distinguishabilities form at most two closed intervals, which can be separated by a gap. The intervals arise from opposite axial marker polarizations with the same fringe-amplitude modulus.