Manuscript Oai272-A@1 · Oai272-A.tex · example · a40828a0

Example: Dropping the public record manufactures apparent secrecy

Conditioning, implementation error, and protocol restrictions · lines 1078–1094

Let

τ = \frac{1}{2} i = 0 \sum^{1} ∣ i, i ⟩ ⟨ i, i ∣_{K_{A} K_{B}} \otimes ∣ i ⟩ ⟨ i ∣_{T} .

Discarding $T$ gives a perfect uniform correlated bit. With $T$ retained, however,

σ in f ∥ τ - γ^{(1)}_{σ} ∥_{1} = 1.

Indeed, dephase $σ$ in the transcript basis. For either transcript value, the sum of the two classical absolute differences is $1/2$ , independently of that transcript's comparison probability. Summing gives one, and the uniform comparison law attains it.

Displayed formulas in this passage

unlabeled · line 1080
$τ = \frac{1}{2} i = 0 \sum^{1} ∣ i, i ⟩ ⟨ i, i ∣_{K_{A} K_{B}} \otimes ∣ i ⟩ ⟨ i ∣_{T} .$
unlabeled · line 1086
$σ in f ∥ τ - γ^{(1)}_{σ} ∥_{1} = 1.$

Nearby in this section

proposition: Proposition: Public conditioning and aborts
proposition: Proposition: Complete-interface robustness
section: Conditioning, implementation error, and protocol restrictions
proposition: Proposition: Restriction is not a new impossibility theorem
section: Conditioning, implementation error, and protocol restrictions