Complete coherent preservation

The complete program is

Its body is

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

Here new abbreviates the required finite pure allocation. The preparation and evolution are specified unitary extensions. Together they realize $U_{\mathrm{body},t}$ on the encoded input.

There is no $\mathsf{Enter}$ in this coherent body. Its logical denotation is ${\hat{\mathcal{V}}}_t$. The global restore map is (eq:restore); in finite dimension it is realizable by Proposition prop:finite-realization. This is the typed reading of complete preservation in CheungHawk04A,CheungEn03A.

The program begins after the carrier dictionary and preparation map have been defined. It constructs neither a quantum field nor a metric.