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

Example: Missing sector probabilities

Stage B: centers and restricted preparations › Center-sensitive affine snapshots · lines 581–596

En05-C@1#ex:missingcenter

Let $A = M_{2} \oplus M_{2}$ , and fix a density matrix $ρ$ . The states

η_{p} = pρ \oplus (1 - p) ρ, 0 < p < 1,

have the same normalized state $ρ$ in both sectors. Nevertheless the central projection $e_{+} = (1, 0)$ has

η_{p} (e_{+}) = p .

Thus a complete central readout distinguishes $p = 1/4$ from $p = 3/4$ . The finite gauge example below realizes these states as restrictions of physical global states.

Displayed formulas in this passage

unlabeled · line 585
$η_{p} = pρ \oplus (1 - p) ρ, 0 < p < 1,$
unlabeled · line 590
$η_{p} (e_{+}) = p .$

Nearby in this section

section: Center-sensitive affine snapshots
proposition: Proposition: Finite center-sensitive snapshot
section: Center-sensitive affine snapshots