Manuscript Hawk04-A@1 · Hawk04-A.tex · remark · 526092ba

Remark: Repair to an unrestricted S tV t argument

Endpoints and the missing gravitational implications › Access-preserving output identifications · lines 1888–1903

A general output unitary $S_{t}$ that mixes radiation and residual does not preserve the original recovery task. For example,

V ∣ ψ ⟩ = ∣ 0 ⟩_{R} ∣ ψ ⟩_{B}

has leakage $a_{d}$ , whereas a swap of $R$ and $B$ produces zero leakage in the new partition.

A derived scattering representation may define a legitimate new asymptotic access algebra, as in Hawk02-D CheungHawk02D. Its relation to finite-time access must nevertheless be proved. Strong convergence alone does not supply that relation.

Displayed formulas in this passage

unlabeled · line 1892
$V ∣ ψ ⟩ = ∣ 0 ⟩_{R} ∣ ψ ⟩_{B}$

Nearby in this section

definition: Definition: Access-preserving common output space
lemma: Lemma: Local isometric embeddings preserve leakage
theorem: Theorem: Endpoint continuity with the access condition retained