Manuscript Hawk04-B@2 · Hawk04-B.tex · section · ba3b0713

A local quantum decoder

Explicit programs and their output ledgers › A local quantum decoder · lines 821–855

For a specified finite CPTP decoder, the local program is

P_{D} : Q_{R} ⟶ Q_{C}^{out},

with body

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

All unused work wires are included in $G$ . The program consumes syndrome/work qubits, not the diary output. This interface is consistent with the quantum-return decoder programs in CheungEn02B.

Applying this program locally to the coherent output gives

P_{keep, t} = (P_{D} \otimes id_{Q_{B}}) P_{coh, t} : Q_{C} ⟶ Q_{C}^{out} \otimes Q_{B} .

Its body returns (Cout,B). The observer who controls only the first returned factor sees

D N_{t} .

Thus radiation-only access is a declared marginal of a complete output, not an implicit rule deleting a live quantum wire.

Displayed formulas in this passage

unlabeled · line 824
$P_{D} : Q_{R} ⟶ Q_{C}^{out},$
unlabeled · line 841
$P_{keep, t} = (P_{D} \otimes id_{Q_{B}}) P_{coh, t} : Q_{C} ⟶ Q_{C}^{out} \otimes Q_{B} .$
unlabeled · line 850
$D N_{t} .$