Manuscript Hawk04-C@1 · Hawk04-C-v1.tex · example · 94d46352

Example: An explicit relocation and its opposite

Row 1: the collapse analogy · lines 619–648 · proof included or linked

Hawk04-C@1#ex:relocation, Hawk04-C@1#eq:hidden-visible

Let $R ≃ B ≃ C$ and define

V_{hidden} ∣ ψ ⟩ = ∣ 0 ⟩_{R} ∣ ψ ⟩_{B}, V_{visible} ∣ ψ ⟩ = ∣ ψ ⟩_{R} ∣ 0 ⟩_{B} .

Both are complete isometries. The first has residual-only relocation and constant accessible output. The second has exact accessible recovery and constant residual output. For qubit registers, the first can be obtained by a specified SWAP with a blank register.

Proof. For $V_{hidden}$ ,

N_{hidden} (X) = Tr (X) ∣ 0 ⟩ ⟨ 0 ∣, E_{hidden} (X) = X .

The formulas are interchanged for $V_{visible}$ . They establish the assertions on all operators and references.

Displayed formulas in this passage

Hawk04-C@1#eq:hidden-visible · line 622
$V_{hidden} ∣ ψ ⟩ = ∣ 0 ⟩_{R} ∣ ψ ⟩_{B}, V_{visible} ∣ ψ ⟩ = ∣ ψ ⟩_{R} ∣ 0 ⟩_{B} .$
unlabeled · line 641
$N_{hidden} (X) = Tr (X) ∣ 0 ⟩ ⟨ 0 ∣, E_{hidden} (X) = X .$

Example: An explicit relocation and its opposite

Displayed formulas in this passage

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