Estimation of Quantum Umlaut Information
Abstract
Quantifying correlations is important for understanding how quantum states and channels support information processing. Quantum umlaut information U connects such correlations to reliability in hypothesis testing and certain communication settings, but its known formulas require classical descriptions of the underlying states. To estimate correlations without these descriptions, we introduce measured quantum umlaut information UM by replacing Umegaki relative entropy with measured relative entropy. Its variational formulation leads to a quantum generative adversarial framework for estimating UM from measurement statistics of unknown bipartite states and classical-quantum channels. This framework optimizes reference states and measurements without reconstructing the target states or channel outputs. For classical-quantum channels, it also optimizes the input probabilities. We further analyze the relation between UM and U, deriving a state-dependent gap bound and characterizing equality for full-rank bipartite states. Numerical simulations show trained estimates close on average to independently computed numerical references for UM across the tested states and channels. These estimates could help assess how well quantum memories preserve correlations and how noise or drift affects input-output dependence in quantum transmitters and state-preparation devices.
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BibTeX
@misc{kim2026estimation,
title = {{Estimation of Quantum Umlaut Information}},
author = {Beomjoon Kim and Donghwa Ji and Kabgyun Jeong},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41282},
eprint = {2610.41282},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41282},
}
RIS
TY - UNPB
TI - Estimation of Quantum Umlaut Information
AU - Beomjoon Kim
AU - Donghwa Ji
AU - Kabgyun Jeong
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41282
UR - https://arxiv.org/abs/2610.41282
AB - Quantifying correlations is important for understanding how quantum states and channels support information processing. Quantum umlaut information U connects such correlations to reliability in hypothesis testing and certain communication settings, but its known formulas require classical descriptions of the underlying states. To estimate correlations without these descriptions, we introduce measured quantum umlaut information U^M by replacing Umegaki relative entropy with measured relative entropy. Its variational formulation leads to a quantum generative adversarial framework for estimating U^M from measurement statistics of unknown bipartite states and classical-quantum channels. This framework optimizes reference states and measurements without reconstructing the target states or channel outputs. For classical-quantum channels, it also optimizes the input probabilities. We further analyze the relation between U^M and U, deriving a state-dependent gap bound and characterizing equality for full-rank bipartite states. Numerical simulations show trained estimates close on average to independently computed numerical references for U^M across the tested states and channels. These estimates could help assess how well quantum memories preserve correlations and how noise or drift affects input-output dependence in quantum transmitters and state-preparation devices.
ER -