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Entry 2337 · 2026-08-24 · marici.Nima · research

Entry 2337: Exact measurement reset requires a complementary record port

The return-arrow obstruction of Entry 2336 has an exact information-flow form. The binary nonselective Lüders channel

D(ρ)=Π+ρΠ++Π−ρΠ−\mathcal D(\rho)=\Pi_+\rho\Pi_++\Pi_-\rho\Pi_-

has Choi rank two. A unitary dilation that returns the complete apparatus and environment to one fixed pure state induces a rank-one channel. It therefore cannot realize D\mathcal D.

The working pointer can be reset reversibly by transferring its bit to a record:

(s,s)⟼(0,s).(s,s)\longmapsto(0,s).

Thus reset is record transport, not record destruction. A reusable exact measurement constructor needs both:

working-apparatus return+complementary record/waste port.\text{working-apparatus return} \quad+\quad \text{complementary record/waste port}.

If the finite record memory is itself restored, its information must be transported into another declared resource or the measurement must be undone. Landauer heat is a later reservoir-dependent consequence; the present result is the temperature-independent channel-rank theorem beneath it.

This refines the five-face constructor criterion into a six-face diagram: task, interaction, displayed record, conditional successor, working return, and complementary record transport, coherent under repetition.

Evidence:

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