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

Example: A record plus a quantum early register can recover

Enter, surviving early quantum access, and teleportation · lines 1413–1438

Hawk06-A@1#ex:teleport

Take $h = d$ and the fixed resource $∣ Φ_{d} ⟩_{H E}$ . A Bell-basis transform on $L H$ , followed by release of those two registers, has the expansion

V_{tel} ∣ ψ ⟩ = \frac{1}{d} z \sum ∣ z ⟩_{R} W_{z} ∣ ψ ⟩_{E} ∣ 0 ⟩_{B},

with appropriate fixed Pauli phase conventions. One may include an untouched two-dimensional spectator $B$ prepared in $∣ 0 ⟩$ , so the residual space is positive dimensional.

Enter on $R$ gives

M (X) = \frac{1}{d ^{2}} z \sum ∣ z ⟩ ⟨ z ∣_{Y} \otimes W_{z} X W_{z}^{†} .

Reading $z$ and applying $W_{z}^{†}$ to the surviving quantum $E$ exactly returns $X$ , including external references. The classical record $Y$ alone is independent of $X$ and cannot recover it.

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unlabeled · line 1418
$V_{tel} ∣ ψ ⟩ = \frac{1}{d} z \sum ∣ z ⟩_{R} W_{z} ∣ ψ ⟩_{E} ∣ 0 ⟩_{B},$
unlabeled · line 1429
$M (X) = \frac{1}{d ^{2}} z \sum ∣ z ⟩ ⟨ z ∣_{Y} \otimes W_{z} X W_{z}^{†} .$

Example: A record plus a quantum early register can recover

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