Manuscript VII-A-ST@1 · VII-A-ST.tex · section · c39a67a3

Finite encoding and the destructive-clock instrument

Finite encoding and the destructive-clock instrument · lines 1556–1591

VII-A-ST@1#eq:effects, VII-A-ST@1#eq:scoreidentity

Let the sample payload be two qubits,

H_{X} = C^{4}, A_{s} = a = 0 \sum^{3} b_{s a} ∣ a ⟩ ⟨ a ∣_{X} .

The sample basis labels classical entries of (eq:finite-table); it is not a one-particle basis of a scalar or gravitational field.

Choose a declared real calibration

Λ > 2 s, a max ∣ b_{s a} ∣.

Define a binary table probe by

E_{s, y} = \frac{1}{2} (I + y A_{s} /Λ), M_{s, y} = E_{s, y}^{1/2}, y = \pm 1.

These satisfy

y \sum M_{s, y}^{†} M_{s, y} = I, y \sum Λ y E_{s, y} = A_{s} .

On input $∣ a ⟩ ⟨ a ∣$ at setting $s$ , the score $Λ y$ has mean $b_{s a}$ .

The finite constants are prescribed real metadata. Their appearance in a finite model does not assert that arbitrary real calibration data have been obtained exactly in finite physical precision.

Displayed formulas in this passage

VII-A-ST@1#eq:scoreidentity · line 1579
$y \sum M_{s, y}^{†} M_{s, y} = I, y \sum Λ y E_{s, y} = A_{s} .$
unlabeled · line 1560
$H_{X} = C^{4}, A_{s} = a = 0 \sum^{3} b_{s a} ∣ a ⟩ ⟨ a ∣_{X} .$
unlabeled · line 1569
$Λ > 2 s, a max ∣ b_{s a} ∣.$
VII-A-ST@1#eq:effects · line 1573
$E_{s, y} = \frac{1}{2} (I + y A_{s} /Λ), M_{s, y} = E_{s, y}^{1/2}, y = \pm 1.$