Manuscript Hawk04-D@1 · Hawk04-D-v1.tex · section · 39b16f67

An independent thermal-pair cutoff

Thermal calibration is not a complete emission channel › An independent thermal-pair cutoff · lines 1163–1185

Use $ℏ = k_{B} = 1$ in this subsection. For one oscillator frequency $ω > 0$ , temperature $T > 0$ , and $λ = e^{- ω / T}$ , define

∣ Θ_{λ} ⟩ = 1 - λ r = 0 \sum^{\infty} λ^{r /2} ∣ r ⟩_{T} ∣ r ⟩_{P} .

Its $T$ -marginal is

τ_{λ} = (1 - λ) r = 0 \sum^{\infty} λ^{r} ∣ r ⟩ ⟨ r ∣, Tr (N τ_{λ}) = \frac{λ}{1 - λ} .

The normalized cutoff preparation is

∣ Θ_{λ, m} ⟩ = \frac{1 - λ}{1 - λ ^{m + 1}} r = 0 \sum^{m} λ^{r /2} ∣ r ⟩_{T} ∣ r ⟩_{P} .

Displayed formulas in this passage

unlabeled · line 1168
$∣ Θ_{λ} ⟩ = 1 - λ r = 0 \sum^{\infty} λ^{r /2} ∣ r ⟩_{T} ∣ r ⟩_{P} .$
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$τ_{λ} = (1 - λ) r = 0 \sum^{\infty} λ^{r} ∣ r ⟩ ⟨ r ∣, Tr (N τ_{λ}) = \frac{λ}{1 - λ} .$
unlabeled · line 1179
$∣ Θ_{λ, m} ⟩ = \frac{1 - λ}{1 - λ ^{m + 1}} r = 0 \sum^{m} λ^{r /2} ∣ r ⟩_{T} ∣ r ⟩_{P} .$