Manuscript Em03-E@1 · Em03-E-v1.tex · section · c4b07e6a

Ciphertext emission

E1: explicit internal and emission Hamiltonians › Ciphertext emission · lines 499–530

Em03-E@1#eq:cipheremission

Define

T_{2} = x = 0 \sum^{1} ∣ 0, 0 ⟩_{F_{2} Q} ⟨ 1, x ∣ \otimes ∣ x_{o} ⟩_{C_{2}} ⟨ v ∣, G_{2} = T_{2} + T_{2}^{†} .

Use a pulse area $0 \leq θ \leq π /2$ , and set

p = sin^{2} θ .

Then

∣ 1, x ⟩_{F_{2} Q} ∣ v ⟩_{C_{2}} ⟼ 1 - p ∣ 1, x ⟩_{F_{2} Q} ∣ v ⟩_{C_{2}} - i p ∣ 0, 0 ⟩_{F_{2} Q} ∣ x_{o} ⟩_{C_{2}} .

The same source state $∣ 0, 0 ⟩_{F_{2} Q}$ appears for both successful message basis states. This is the coherence-preserving part of the emission.

Both $T_{i}$ are partial isometries with orthogonal initial and final subspaces, so $G_{i}$ are self-adjoint with norm one. Their action on every unpaired basis state is zero. The model therefore specifies the full Hamiltonians, not merely an isometry with an unspecified unitary extension.

Displayed formulas in this passage

Em03-E@1#eq:cipheremission · line 514
$∣ 1, x ⟩_{F_{2} Q} ∣ v ⟩_{C_{2}} ⟼ 1 - p ∣ 1, x ⟩_{F_{2} Q} ∣ v ⟩_{C_{2}} - i p ∣ 0, 0 ⟩_{F_{2} Q} ∣ x_{o} ⟩_{C_{2}} .$
unlabeled · line 502
$T_{2} = x = 0 \sum^{1} ∣ 0, 0 ⟩_{F_{2} Q} ⟨ 1, x ∣ \otimes ∣ x_{o} ⟩_{C_{2}} ⟨ v ∣, G_{2} = T_{2} + T_{2}^{†} .$
unlabeled · line 510
$p = sin^{2} θ .$