Manuscript Hawk03-A@1 · Hawk03-A.tex · section · 9a109c12

Independent-factor AMPS benchmarks

Independent-factor AMPS benchmarks · lines 273–299

Hawk03-A@1#eq:gd

Let $A$ denote a proposed partner, $B$ a selected outgoing packet, and $E$ previously accessible radiation. This section assumes a genuine tensor product

H_{A} \otimes H_{B} \otimes H_{E}

and one joint density operator on it. This is an explicit hypothesis, not a consequence of the names “interior” and “radiation.”

All logarithms in entropy expressions are base two. Set

S (X)_{ρ} = - Tr (ρ_{X} lo g_{2} ρ_{X}), S (B ∣ A)_{ρ} = S (A B)_{ρ} - S (A)_{ρ} .

For $0 \leq x \leq 1$ , define

h_{2} (x) = - x lo g_{2} x - (1 - x) lo g_{2} (1 - x),

with the usual zero conventions, and

g_{d} (x) = 2 x lo g_{2} d + (1 + x) h_{2} (\frac{x}{1 + x}) .

Displayed formulas in this passage

Hawk03-A@1#eq:gd · line 294
$g_{d} (x) = 2 x lo g_{2} d + (1 + x) h_{2} (\frac{x}{1 + x}) .$
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$H_{A} \otimes H_{B} \otimes H_{E}$
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$S (X)_{ρ} = - Tr (ρ_{X} lo g_{2} ρ_{X}), S (B ∣ A)_{ρ} = S (A B)_{ρ} - S (A)_{ρ} .$
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$h_{2} (x) = - x lo g_{2} x - (1 - x) lo g_{2} (1 - x),$

Independent-factor AMPS benchmarks

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