Sharper localisation rates for QMI change-point estimation

Derive sharper localisation rates for the quantum mutual-information change-point estimator, beyond the consistency results established for the unstudentised criterion.

Background

The paper proves detection and localisation consistency for an unstudentised quantum mutual-information criterion under an identifiability condition, but the deployed estimator maximises a permutation-studentised curve. The authors report empirical localisation errors without a monotone trend and explicitly identify sharper localisation rates as unresolved.

References

The main open problems are theoretical: sharper localisation rates; the mixing-case extension of the process-level Proposition P2′ of Appendix A.6, which needs an invariance principle for bounded strongly mixing sequences [41]; a limit theory for the studentised scan, whose null law stabilises across sample sizes in Supplementary Section B.3; consistency of Holevo-PELT in the number of segments, whose expected behaviour Supplementary Section B.3 also reports; and a detection-delay lower bound via the quantum Fisher information, for which Section 3.4 is the first step.

— Quantum mutual information statistics for detecting dependence-structure change points in time series  (2609.02787 - Kang et al., 2 Sep 2026) in Section 7, Discussion; Appendix A.7

The main open problems are theoretical: sharper localisation rates; the mixing-case extension of the process-level Proposition P2′ of Appendix A.6, which needs an invariance principle for bounded strongly mixing sequences [41]; a limit theory for the studentised scan, whose null law stabilises across sample sizes in Supplementary Section B.3; consistency of Holevo-PELT in the number of segments, whose expected behaviour Supplementary Section B.3 also reports; and a detection-delay lower bound via the quantum Fisher information, for which Section 3.4 is the first step.

— Quantum mutual information statistics for detecting dependence-structure change points in time series  (2609.02787 - Kang et al., 2 Sep 2026) in Section 7, Discussion; Appendix A.12; Supplementary Section B.3

The main open problems are theoretical: sharper localisation rates; the mixing-case extension of the process-level Proposition P2′ of Appendix A.6, which needs an invariance principle for bounded strongly mixing sequences [41]; a limit theory for the studentised scan, whose null law stabilises across sample sizes in Supplementary Section B.3; consistency of Holevo-PELT in the number of segments, whose expected behaviour Supplementary Section B.3 also reports; and a detection-delay lower bound via the quantum Fisher information, for which Section 3.4 is the first step.

— Quantum mutual information statistics for detecting dependence-structure change points in time series  (2609.02787 - Kang et al., 2 Sep 2026) in Section 7, Discussion; Supplementary Section B.3

The main open problems are theoretical: sharper localisation rates; the mixing-case extension of the process-level Proposition P2′ of Appendix A.6, which needs an invariance principle for bounded strongly mixing sequences [41]; a limit theory for the studentised scan, whose null law stabilises across sample sizes in Supplementary Section B.3; consistency of Holevo-PELT in the number of segments, whose expected behaviour Supplementary Section B.3 also reports; and a detection-delay lower bound via the quantum Fisher information, for which Section 3.4 is the first step.

— Quantum mutual information statistics for detecting dependence-structure change points in time series  (2609.02787 - Kang et al., 2 Sep 2026) in Section 7, Discussion; Section 3.4