Separating geometry from information at matched record information

Determine whether channel-equivalent monitoring instruments with exactly matched full record Fisher information can nevertheless produce distinct peak-control accuracy costs through differences in conditional noise geometry.

Background

The paper’s principal comparison changes both the orientation of measurement backaction relative to the target manifold and the information content of the public record. Within the one-parameter instrument family studied, equality of the full local Fisher quadratic form forces equality of the parameter δ\delta, so the construction does not isolate geometry while holding information fixed. The authors explicitly leave open whether the feedback-cost separation persists for instruments with exactly matched information.

References

It does not identify their exact mixed-state optimum, its dependence on the peak $U$, or a matching attainable policy.

— Distinct Feedback-Strength Requirements for Quantum-State Ensemble Preparation under Channel-Equivalent Monitoring  (2609.31221 - Huang et al., 25 Sep 2026) in Supplemental Material, Section \ref{sec:S-efficiency}, paragraph following Eq. (\ref{eq:S-complete-Pauli-efficiency-window}); reiterated in Section \ref{sec:S-efficiency} scope discussion

The present readouts vary geometry and record information jointly; separating their contributions at exactly matched information remains open.

— Distinct Feedback-Strength Requirements for Quantum-State Ensemble Preparation under Channel-Equivalent Monitoring  (2609.31221 - Huang et al., 25 Sep 2026) in Conclusion, final paragraph before \texttt{\textbackslash nocite}; see also Supplemental Material, Section \ref{sec:S-multiqubit}