Manuscript En05-C@1 · En05-C.tex · example · aa213ea6

Example: Containment with genuine local dependence

Stage D: a finite constrained Z2 model › Four operational tests · lines 1073–1098

En05-C@1#ex:localread

Set $P_{\pm} = (1 \pm Q) /2$ . The supported Kraus operators $P_{\pm}$ commute with the Gauss constraint. The complete recorded instrument is

T (a_{+}, a_{-}) = P_{+} a_{+} P_{+} + P_{-} a_{-} P_{-} .

On the local recorded output $A ({1, 2}) \oplus A ({1, 2})$ , its range is in $A ({1, 2})$ . The scalar report channel has effects $P_{+}, P_{-}$ and distinguishes the physical inputs $∣ f, + ⟩$ and $∣ f, - ⟩$ with gap one. Thus containment does not imply a constant output.

The nonselective channel acts on the local basis by

T_{ns} (e_{f}) = e_{f}, T_{ns} (e_{f} Q) = e_{f} Q, T_{ns} (e_{f} R) = 0, T_{ns} (e_{f} QR) = 0.

These formulas test containment on a complete spanning set.

Displayed formulas in this passage

unlabeled · line 1078
$T (a_{+}, a_{-}) = P_{+} a_{+} P_{+} + P_{-} a_{-} P_{-} .$
unlabeled · line 1091
$T_{ns} (e_{f}) = e_{f}, T_{ns} (e_{f} Q) = e_{f} Q, T_{ns} (e_{f} R) = 0, T_{ns} (e_{f} QR) = 0.$

Example: Containment with genuine local dependence

Displayed formulas in this passage

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