Manuscript Hawk01-B@1 · Hawk01-B.tex · section · cfa976f1

Weyl operators and the first emission

Internally generated key and sequential logical transfer › Weyl operators and the first emission · lines 718–743

Hawk01-B@1#eq:firstemission, Hawk01-B@1#eq:earlymarginal

The first emission is

V_{1} ∣ ψ ⟩_{A} = \frac{1}{d} r \sum ∣ f, r; U_{r} ψ ⟩_{B_{1}} \otimes ∣ r ⟩_{R_{1}} .

Here $∣ f, r; ψ ⟩$ is a linear isometric embedding of the logical vector into the pending residual summand labelled by $r$ . All pending residual states have energy $M - e_{K}$ .

Equation (eq:firstemission) creates the key correlation inside the evolution. Its coefficient and the $d^{2}$ terms give $V_{1}^{†} V_{1} = I_{A}$ . There is no externally supplied early register or classical random key. The first outgoing marginal is

N_{R_{1}} (Y) = Tr (Y) \frac{I _{d^{2}}}{d ^{2}} .

The complementary output retains the encrypted code and the key.

Displayed formulas in this passage

Hawk01-B@1#eq:firstemission · line 721
$V_{1} ∣ ψ ⟩_{A} = \frac{1}{d} r \sum ∣ f, r; U_{r} ψ ⟩_{B_{1}} \otimes ∣ r ⟩_{R_{1}} .$
Hawk01-B@1#eq:earlymarginal · line 738
$N_{R_{1}} (Y) = Tr (Y) \frac{I _{d^{2}}}{d ^{2}} .$

Weyl operators and the first emission

Displayed formulas in this passage

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