Manuscript X-J-ST@1 · X-J-ST.tex · section · 8f0d1a36

The complete finite clock

Section C: complete destructive instruments and the positive gap › The complete finite clock · lines 1400–1411

Let $C ≅ C^{2^{q}}$ have a calibrated orthonormal basis ${∣ τ_{k} ⟩}$ , and let $B_{C} ∣ τ_{k} ⟩ = ∣ k ⟩$ . For an arbitrary surviving interface $A$ , define

D_{k} = ⟨ τ_{k} ∣_{C} \otimes I_{A}, T_{C} (Z) = k \sum ∣ k ⟩ ⟨ k ∣_{R_{C}} \otimes D_{k} Z D_{k}^{†} .

Displayed formulas in this passage

unlabeled · line 1405
$D_{k} = ⟨ τ_{k} ∣_{C} \otimes I_{A}, T_{C} (Z) = k \sum ∣ k ⟩ ⟨ k ∣_{R_{C}} \otimes D_{k} Z D_{k}^{†} .$

Nearby in this section

theorem: Theorem: Destructive clock and combined instrument
section: The complete finite clock