Optimal filtering operations for dynamical steering and measurement incompatibility

Determine the optimal pre- and post-filtering operations within the dynamical frameworks of quantum steering and measurement incompatibility for achieving activation and distillation objectives.

Background

The paper demonstrates that pre-filtering alone cannot activate an incompatibility-annihilating (IA) channel, whereas post-filtering can stochastically activate IA channels. Combining pre- and post-filtering operations can both activate and distill measurement-incompatibility preservability. For the numerical demonstration, the authors use particular diagonal Kraus operators for the pre- and post-filters rather than deriving filters that are optimal for the relevant robustness measures.

The unresolved problem is to characterize optimal local filtering operations in the dynamical settings of quantum steering and measurement incompatibility, extending prior work on optimal filtering for related steering and measurement-incompatibility robustness quantities.

References

We conclude with a few open questions. In Refs., the optimal local filtering operations for a series of steering robustness are characterized to achieve the equivalent relation with the corresponding measurement incompatibility robustness. Here, we adopt the pre- and post-filtering operation in Eqs.~eq:pre filter and~eq:post filter for demonstrating IA activation and distillation. How to obtain the optimal filtering operations in the dynamical frameworks of quantum steering and measurement incompatibility?

— Preservability of Measurement Incompatibility: Purification, Activation, and a No-Go Theorem  (2610.01327 - Wu et al., 1 Oct 2026) in Section Conclusions