Manuscript VII-E-ST@1 · VII-E-ST.tex · section · d28d9c5d

Equal terminal slices with unequal residuals

Equal terminal slices with unequal residuals · lines 1785–1811

VII-E-ST@1#eq:path-table

The following exact specialization connects the two contracts without identifying them.

Take $B = 2$ , start at $(0, 0)$ , and choose $η = 3/5$ . Then

M_{+} = diag (1, 2) / 5, M_{-} = diag (2, 1) / 5 .

The two-step path Kraus operators are

h = (a_{1}, a_{2}) + + + - - + - - q_{2} 200 - 2 L_{h} e^{- 3 π i Q /8} diag (1, 4) /5 (2/5) e^{- π i Q /8} (2/5) e^{+ π i Q /8} e^{+ 3 π i Q /8} diag (4, 1) /5

Their effects sum to $I$ : the two outer effects are $diag (1, 16) /25$ , $diag (16, 1) /25$ , and each middle effect is $4 I /25$ .

Displayed formulas in this passage

VII-E-ST@1#eq:path-table · line 1798
$h = (a_{1}, a_{2}) + + + - - + - - q_{2} 200 - 2 L_{h} e^{- 3 π i Q /8} diag (1, 4) /5 (2/5) e^{- π i Q /8} (2/5) e^{+ π i Q /8} e^{+ 3 π i Q /8} diag (4, 1) /5$
unlabeled · line 1793
$M_{+} = diag (1, 2) / 5, M_{-} = diag (2, 1) / 5 .$