Manuscript VII-E@1 · VII-E.tex · example · b713cf3c

Example: A qubit incompatibility

Record compatibility, residuals, and composition › The exact unassisted record error · lines 1213–1224

Let $T (ρ) = H ρ H$ , where $H$ is the Hadamard unitary. Use computational-basis measurements before and after $T$ , with identity label aggregation. Then

D_{0} = \frac{X - Z}{2}, D_{1} = - D_{0}, δ_{rec} = \frac{1}{2} .

The state $∣ 0 ⟩ ⟨ 0 ∣$ gives error $1/2$ , so it is not a worst-case input.

Displayed formulas in this passage

unlabeled · line 1217
$D_{0} = \frac{X - Z}{2}, D_{1} = - D_{0}, δ_{rec} = \frac{1}{2} .$

Nearby in this section

section: The exact unassisted record error
theorem: Theorem: Event operator-norm formula
example: Example: Why individual outcomes are insufficient
section: The exact unassisted record error