Manuscript En07-C@1 · En07-C.tex · definition · 3f7e9ebb

Definition: Replacement, recovery, and leakage

The complete finite interface and error conventions · lines 315–344

En07-C@1#def:errors, En07-C@1#eq:recovery-error, En07-C@1#eq:leakage-error

For a density operator $σ$ on a specified output space, define

T_{σ} (X) = Tr (X) σ .

Set

ε_{rec} (N) δ_{leak} (E) = D : R \to C CPTP min d_{⋄} (DN, id_{C}), = σ \in D (B) min d_{⋄} (E, T_{σ}) .

Write

τ_{C} = \frac{I _{C}}{d}, q_{d} = 1 - d^{- 2} .

A decoder is deterministic: it is a completely positive, trace-preserving map on all of $L (R)$ . Postselected success is not substituted for (eq:recovery-error).

Displayed formulas in this passage

En07-C@1#eq:recovery-error · line 322
$ε_{rec} (N) δ_{leak} (E) = D : R \to C CPTP min d_{⋄} (DN, id_{C}), = σ \in D (B) min d_{⋄} (E, T_{σ}) .$
En07-C@1#eq:leakage-error · line 322
$ε_{rec} (N) δ_{leak} (E) = D : R \to C CPTP min d_{⋄} (DN, id_{C}), = σ \in D (B) min d_{⋄} (E, T_{σ}) .$
unlabeled · line 318
$T_{σ} (X) = Tr (X) σ .$
unlabeled · line 335
$τ_{C} = \frac{I _{C}}{d}, q_{d} = 1 - d^{- 2} .$

Definition: Replacement, recovery, and leakage

Displayed formulas in this passage

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