Manuscript Hawk02-A@1 · Hawk02-A.tex · definition · 7fbae745

Definition: Recovery and leakage

Stage 5: exact and approximate information preservation › Complete residual leakage · lines 803–822

Hawk02-A@1#def:leakage, Hawk02-A@1#eq:recerror, Hawk02-A@1#eq:leakage

For Definition def:completeoutput, define

ε_{rec} (N) δ_{leak} (C) = D : A \to C in f d_{⋄} (D \circ N, id_{C}), = τ_{B} in f d_{⋄} (C, T_{τ_{B}}), T_{τ_{B}} (X) = Tr (X) τ_{B},

where the decoder is CPTP and $τ_{B}$ is a density operator. The optimization includes the complete inaccessible output.

Displayed formulas in this passage

Hawk02-A@1#eq:recerror · line 806
$ε_{rec} (N) δ_{leak} (C) = D : A \to C in f d_{⋄} (D \circ N, id_{C}), = τ_{B} in f d_{⋄} (C, T_{τ_{B}}), T_{τ_{B}} (X) = Tr (X) τ_{B},$
Hawk02-A@1#eq:leakage · line 806
$ε_{rec} (N) δ_{leak} (C) = D : A \to C in f d_{⋄} (D \circ N, id_{C}), = τ_{B} in f d_{⋄} (C, T_{τ_{B}}), T_{τ_{B}} (X) = Tr (X) τ_{B},$