Theory of block-induced response and open-close asymmetry

Derive a theory from the composite affine-pair dynamics that explains why blocks of bath-polarisation rounds produce opposite end-margin effects at different schedule positions, why the direct per-round lever can have the opposite sign from the eventual pulse effect, and why window-polarisation rounds in the closing protocol act collectively rather than independently.

Background

The paper analyzes pulsed schedules that switch a composite channel between entanglement-breaking and non-entanglement-breaking behavior. In the opening mode, hot rounds inserted into an intermediate-polarisation hold can restore entanglement; in the closing mode, intermediate-polarisation rounds inserted into a hot hold can destroy it, but typically require substantially more rounds.

Certified calculations show that matched pulse and hold rounds have similar local effects on the running log-margin, while the eventual end-margin response depends strongly on position and on whether the pulse is opening or closing the valve. In particular, end-of-schedule blocks can act in the opposite direction from central blocks, and the direct lever of a pulse round can have the opposite sign from the pulse’s eventual effect. The paper leaves a dynamical explanation of these effects unresolved, beyond attributing them generally to how a block changes the composite affine pair.