Manuscript Em03-H@8 · Em03-H-v8.tex · proposition · 91e9e3bd

Proposition: Complementary diagnostics

Candidate dilation, decoder, and limitations › Specified complete decoder · lines 1369–1397 · proof included or linked

Em03-H@8#prop:candidatebounds

L_{E} = 1 - η^{2}, δ_{E} = \frac{1 - η}{4} (η^{2} + 4 + 1 + 2 η),

\frac{( 1 - η ^{2} ) ^{2}}{4} \leq ε_{rec} (N_{g}) \leq min (3/4, 1 - η, 2 2 δ_{E}) .

Proof. The complementary $Z$ -pair distance is $1 - η^{2}$ , while the $X, Y$ distances are $1 - η$ . With $t = 1 - η$ , the nontrivial Choi-difference block is

(t (1 + η) /4 t /2 t /2 t^{2} /4) .

Its trace norm is $t η^{2} + 4 /2$ . Other diagonal absolute values sum to $t (1/2 + η)$ . Divide by two and apply Theorems thm:complementary and thm:specified.

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unlabeled · line 1371
$L_{E} = 1 - η^{2}, δ_{E} = \frac{1 - η}{4} (η^{2} + 4 + 1 + 2 η),$
unlabeled · line 1376
$\frac{( 1 - η ^{2} ) ^{2}}{4} \leq ε_{rec} (N_{g}) \leq min (3/4, 1 - η, 2 2 δ_{E}) .$
unlabeled · line 1387
$(t (1 + η) /4 t /2 t /2 t^{2} /4) .$

Proposition: Complementary diagnostics

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