Path-Distinguishability Gaps at Fixed Visibility in Noisy Qubit Interferometers
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. Fixing the complex fringe amplitude instead gives a connected interval; for balanced original-path discrimination, a gap requires nonunital marker preparation. For a balanced pure source, relative π rotations, and no subsequent marker noise, we obtain a necessary and sufficient geometric criterion for a gap under some rotation axis perpendicular to the preparation displacement. Explicit channels and a time-independent Lindblad realization show how the gap depends on preparation geometry and evolution, with exact onset and optimization formulas at fixed fractional visibility. We also give sufficient bounds for excluding distinguishability intervals under calibrated finite-resolution errors.
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BibTeX
@misc{siddiqui2026pathdistinguishability,
title = {{Path-Distinguishability Gaps at Fixed Visibility in Noisy Qubit Interferometers}},
author = {Mohd Asad Siddiqui},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33632},
eprint = {2610.33632},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33632},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Path-Distinguishability Gaps at Fixed Visibility in Noisy Qubit Interferometers
AU - Mohd Asad Siddiqui
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.33632
UR - https://arxiv.org/abs/2610.33632
AB - 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. Fixing the complex fringe amplitude instead gives a connected interval; for balanced original-path discrimination, a gap requires nonunital marker preparation. For a balanced pure source, relative π rotations, and no subsequent marker noise, we obtain a necessary and sufficient geometric criterion for a gap under some rotation axis perpendicular to the preparation displacement. Explicit channels and a time-independent Lindblad realization show how the gap depends on preparation geometry and evolution, with exact onset and optimization formulas at fixed fractional visibility. We also give sufficient bounds for excluding distinguishability intervals under calibrated finite-resolution errors.
ER -