Manuscript Hawk06-A@1 · Hawk06-A.tex · section · c59fe67c

The coherent and destructive entropy calculations

The coherent and destructive entropy calculations · lines 1001–1016

Hawk06-A@1#eq:randomprojection

Fix a pure diary input $∣ ψ ⟩$ , independent of the sampled unitary. After tracing $E$ , the vault state is

ρ_{vault}^{U} = \frac{1}{h} U P_{ψ} U^{†}, rank P_{ψ} = h .

Its total entropy is $lo g_{2} h$ . The late-radiation state is its reduction to $R$ .

Displayed formulas in this passage

Hawk06-A@1#eq:randomprojection · line 1006
$ρ_{vault}^{U} = \frac{1}{h} U P_{ψ} U^{†}, rank P_{ψ} = h .$