Manuscript X-Enter-ST@1 · X-Enter-ST.tex · section · f76acc1f

The two-qubit protocol

Stage E: conditional relational input › The two-qubit protocol · lines 1124–1163

X-Enter-ST@1#eq:phaseinput

Freeze

σ > 0, σ^{'} = \frac{r _{ε}}{c _{ε}} σ \neq = 0,

where the second scale may be signed. Define the abstract input family

∣ ψ (a, r)⟩ = \frac{1}{2} (∣ 0 ⟩ + e^{i α} ∣ 1 ⟩) \otimes (∣ 0 ⟩ + e^{i β} ∣ 1 ⟩), α = \frac{a}{σ}, β = \frac{r}{σ ^{'}}, θ = α - β = \frac{I _{rel}}{σ r _{ε}} .

Apply CNOT with the first qubit as control and the second as target, then Hadamard on the first. Destructively read both qubits, giving raw bits $(b, e)$ . Report

(b, e) = (0, 1) \mapsto +, (1, 1) \mapsto -, (0, 0), (1, 0) \mapsto F .

The failure output $F$ is retained. There is no returned signal qubit.

Let

∣ ϕ_{\pm} ⟩ = (∣ 00 ⟩ \pm ∣ 11 ⟩) / 2, ∣ χ_{\pm} ⟩ = (∣ 01 ⟩ \pm ∣ 10 ⟩) / 2 .

Displayed formulas in this passage

X-Enter-ST@1#eq:phaseinput · line 1133
$∣ ψ (a, r)⟩ = \frac{1}{2} (∣ 0 ⟩ + e^{i α} ∣ 1 ⟩) \otimes (∣ 0 ⟩ + e^{i β} ∣ 1 ⟩), α = \frac{a}{σ}, β = \frac{r}{σ ^{'}}, θ = α - β = \frac{I _{rel}}{σ r _{ε}} .$
unlabeled · line 1127
$σ > 0, σ^{'} = \frac{r _{ε}}{c _{ε}} σ \neq = 0,$
unlabeled · line 1150
$(b, e) = (0, 1) \mapsto +, (1, 1) \mapsto -, (0, 0), (1, 0) \mapsto F .$
unlabeled · line 1159
$∣ ϕ_{\pm} ⟩ = (∣ 00 ⟩ \pm ∣ 11 ⟩) / 2, ∣ χ_{\pm} ⟩ = (∣ 01 ⟩ \pm ∣ 10 ⟩) / 2 .$

The two-qubit protocol

Displayed formulas in this passage

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