Manuscript En04-A@1 · En04-A.tex · section · bab77211

Complete coherent body and local quantum return

Typed preparation, coherent programs, and Enter › Complete coherent body and local quantum return · lines 700–742

After a carrier dictionary exists, the coherent body has type

P_{coh} : Q_{C} \to Q_{R} \otimes Q_{B}

and form

a := new; (C,a) := EncodeAndPrepare(C,a); (R,B) := CoherentBody(C,a); returnQ(R,B);

It contains no Enter.

A local decoder has type $P_{D} : Q_{R} \to Q_{C}^{out}$ . A finite CPTP decoder can be implemented semantically by

w := new; (Cout,G) := DecoderUnitary(R,w); y := Enter(G); dropBit(y); returnQ(Cout);

The Kraus isometry

L ∣ ψ ⟩ = j \sum D_{j} ∣ ψ ⟩ ∣ j ⟩_{G}

has a finite unitary extension after allocation. Readout and discard of $G$ give $\sum_{j} D_{j} X D_{j}^{†}$ . The diary output remains quantum.

Applying this decoder locally to the coherent output yields a joint program returning (Cout,B). The observer controlling only Cout sees $DN$ . A radiation marginal is therefore a declared access restriction, not a rule silently deleting a live residual wire.

For non-power-of-two dimensions, all logical spaces are subspaces of padded qubit registers. Physical channels are completed on invalid padded inputs, for example by fixed-state preparation. Such padding does not establish a physical field-to-qubit receiver.

Displayed formulas in this passage

unlabeled · line 703
$P_{coh} : Q_{C} \to Q_{R} \otimes Q_{B}$
unlabeled · line 725
$L ∣ ψ ⟩ = j \sum D_{j} ∣ ψ ⟩ ∣ j ⟩_{G}$