Robust multi-hypothesis quantum-state discrimination under unknown common unitary perturbations via least favorable priors
Abstract
We study robust K-ary quantum-state discrimination when all candidate states are affected by the same unknown common unitary perturbation. The unknown perturbation does not represent the label to be identified, but acts as a nuisance factor that changes the performance of a fixed measurement. We formulate the problem as a minimax decision problem over the possible perturbations and propose using the Bayes-optimal collective measurement associated with a least favorable prior (LFP) on the nuisance-parameter space. For a finite discretization of this space, we show that the LFP can be computed by a semidefinite program and that the corresponding value coincides with the finite-grid minimax success probability. As numerical demonstrations, we consider a binary nonorthogonal qubit model and a nonorthogonal three-state qutrit model with an unknown common unitary perturbation. The LFP-based measurement substantially flattens the success-probability profile and improves the worst-case success probability compared with a reference-point optimal measurement and a uniform-prior Bayes measurement. The resulting LFP concentrates its weight on regions of the nuisance-parameter space that actively limit the robust discrimination performance, thereby providing both a constructive measurement design and a diagnostic description of the difficult nuisance-parameter regimes.
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BibTeX
@misc{fujiki2026robust,
title = {{Robust multi-hypothesis quantum-state discrimination under unknown common unitary perturbations via least favorable priors}},
author = {Daichi Fujiki and Fuyuhiko Tanaka},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04020},
eprint = {2609.04020},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04020},
}
RIS
TY - UNPB
TI - Robust multi-hypothesis quantum-state discrimination under unknown common unitary perturbations via least favorable priors
AU - Daichi Fujiki
AU - Fuyuhiko Tanaka
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.04020
UR - https://arxiv.org/abs/2609.04020
AB - We study robust K-ary quantum-state discrimination when all candidate states are affected by the same unknown common unitary perturbation. The unknown perturbation does not represent the label to be identified, but acts as a nuisance factor that changes the performance of a fixed measurement. We formulate the problem as a minimax decision problem over the possible perturbations and propose using the Bayes-optimal collective measurement associated with a least favorable prior (LFP) on the nuisance-parameter space. For a finite discretization of this space, we show that the LFP can be computed by a semidefinite program and that the corresponding value coincides with the finite-grid minimax success probability. As numerical demonstrations, we consider a binary nonorthogonal qubit model and a nonorthogonal three-state qutrit model with an unknown common unitary perturbation. The LFP-based measurement substantially flattens the success-probability profile and improves the worst-case success probability compared with a reference-point optimal measurement and a uniform-prior Bayes measurement. The resulting LFP concentrates its weight on regions of the nuisance-parameter space that actively limit the robust discrimination performance, thereby providing both a constructive measurement design and a diagnostic description of the difficult nuisance-parameter regimes.
ER -