Quantum Barankin bounds beyond local unbiasedness: Analytic results for Gaussian states via a right-division framework
Abstract
We propose a quantum version of the Barankin bound as an alternative to the quantum Cramér-Rao bound for quantum parameter estimation. The quantum Barankin bound provides a lower bound on the mean squared error of estimators satisfying arbitrarily chosen bias constraints at arbitrarily chosen parameter points. In particular, unbiasedness over the entire parameter space can be imposed, yielding precision limits for globally unbiased quantum parameter estimation. In contrast to the recently derived quantum Barankin bound, which is based on a symmetric division superoperator, our bound is based on a nonsymmetric right-division superoperator. This formulation enables us to find analytic expressions for the Barankin matrix for Gaussian states, which allows for an efficient calculation of the bound. We demonstrate the usefulness of our results by applying them to various examples that exhibit the threshold effect in the few-shot regime, which is invisible to the standard quantum Cramér-Rao bound approach.
Related
- Anisotropic overlap reduction functions for arbitrary equal-arm TDI channels: A fully analytic framework and efficient evaluation
- Tests of general relativity using analytic derivatives of parametrized post-Einsteinian gravitational waveforms within the Fisher-matrix framework
- CosmoDyn: a semi-analytic post-processing framework for the dynamical evolution of compact stellar systems and black holes in cosmological simulations
- A New Framework for Interfacial Statistics: Exact n-Point Correlations of Gaussian Level Sets
- A Unified Framework for Bell-Shaped Gaussian Quadratures in Deterministic Boltzmann Solvers
BibTeX
@misc{reichert2026quantum,
title = {{Quantum Barankin bounds beyond local unbiasedness: Analytic results for Gaussian states via a right-division framework}},
author = {Maximilian Reichert and Javier Navarro and Gerardo Adesso and Manuel Gessner and Mikel Sanz},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10157},
eprint = {2609.10157},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10157},
}
RIS
TY - UNPB
TI - Quantum Barankin bounds beyond local unbiasedness: Analytic results for Gaussian states via a right-division framework
AU - Maximilian Reichert
AU - Javier Navarro
AU - Gerardo Adesso
AU - Manuel Gessner
AU - Mikel Sanz
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10157
UR - https://arxiv.org/abs/2609.10157
AB - We propose a quantum version of the Barankin bound as an alternative to the quantum Cramér-Rao bound for quantum parameter estimation. The quantum Barankin bound provides a lower bound on the mean squared error of estimators satisfying arbitrarily chosen bias constraints at arbitrarily chosen parameter points. In particular, unbiasedness over the entire parameter space can be imposed, yielding precision limits for globally unbiased quantum parameter estimation. In contrast to the recently derived quantum Barankin bound, which is based on a symmetric division superoperator, our bound is based on a nonsymmetric right-division superoperator. This formulation enables us to find analytic expressions for the Barankin matrix for Gaussian states, which allows for an efficient calculation of the bound. We demonstrate the usefulness of our results by applying them to various examples that exhibit the threshold effect in the few-shot regime, which is invisible to the standard quantum Cramér-Rao bound approach.
ER -