Manuscript Hawk05-B@1 · Hawk05-B.tex · section · f2e5d4f5

The corrected single-excitation calibration

Explicit entropy–recovery separations › The corrected single-excitation calibration · lines 1219–1250

For comparison with Hawk05-A and Hawk02-B, let each memory and emission cell have space $C ∣ \emptyset ⟩ \oplus C$ . At opportunity $j$ , rotate

∣ i, \emptyset ⟩ ⟼ cos θ_{j} ∣ i, \emptyset ⟩ + sin θ_{j} ∣ \emptyset, i ⟩,

with the complementary rotation on $∣ \emptyset, i ⟩$ . The occupied labels are degenerate, so the rotation conserves the sum of occupied-sector energies.

Set

q_{n} = j = 1 \prod^{n} cos^{2} θ_{j}, p_{j} = q_{j - 1} - q_{j} .

The complete isometry has the form

V_{n} ∣ ψ ⟩ = 1 - q_{n} J_{n} ∣ ψ ⟩_{R} ∣ \emptyset ⟩_{M} + q_{n} ∣ \emptyset ⟩_{R} ∣ ψ ⟩_{M},

where the normalized emission amplitudes define an isometry $J_{n}$ .

Displayed formulas in this passage

unlabeled · line 1225
$∣ i, \emptyset ⟩ ⟼ cos θ_{j} ∣ i, \emptyset ⟩ + sin θ_{j} ∣ \emptyset, i ⟩,$
unlabeled · line 1237
$q_{n} = j = 1 \prod^{n} cos^{2} θ_{j}, p_{j} = q_{j - 1} - q_{j} .$
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$V_{n} ∣ ψ ⟩ = 1 - q_{n} J_{n} ∣ ψ ⟩_{R} ∣ \emptyset ⟩_{M} + q_{n} ∣ \emptyset ⟩_{R} ∣ ψ ⟩_{M},$

The corrected single-excitation calibration

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