Manuscript En02-C@1 · En02-C-v1.tex · section · 7549c6df

C3: an optimal approximate memory obstruction

C3: an optimal approximate memory obstruction · lines 742–768

En02-C@1#eq:omega

The lower bound is stated for all permitted one-live-qubit protocols. It does not require approximate uniqueness of a full-input recovery channel.

Let

ω_{R 123} = (id_{R} \otimes N_{3}) ∣ Φ_{2} ⟩ ⟨ Φ_{2} ∣ .

From (eq:N3),

ω_{R 123} = \frac{1}{16} (I - X_{R} Z_{1} X_{2} Z_{3} + Y_{R} X_{1} Y_{2} X_{3} - Z_{R} Y_{1} Z_{2} Y_{3}) .

Displayed formulas in this passage

En02-C@1#eq:omega · line 757
$ω_{R 123} = \frac{1}{16} (I - X_{R} Z_{1} X_{2} Z_{3} + Y_{R} X_{1} Y_{2} X_{3} - Z_{R} Y_{1} Z_{2} Y_{3}) .$
unlabeled · line 750
$ω_{R 123} = (id_{R} \otimes N_{3}) ∣ Φ_{2} ⟩ ⟨ Φ_{2} ∣ .$