Manuscript En09-A@1 · En09-A.tex · section · eafec9de

Stationarity and the stronger constraint

Frozen native data and measurement semantics › Stationarity and the stronger constraint · lines 268–293

En09-A@1#eq:constraint, En09-A@1#eq:stationarity, En09-A@1#eq:strong-constraint

Fix self-adjoint finite matrices $H_{C}$ and $H_{S}$ , and put

K = H_{C} \otimes I_{S} + I_{C} \otimes H_{S} .

A density operator is stationary when

[K, ρ_{C S}] = 0.

A stronger zero-constraint preparation satisfies

K ρ_{C S} = 0.

For a positive density operator, (eq:strong-constraint) means that its support lies in $ker K$ , and implies (eq:stationarity). For a pure preparation the stronger condition is $K ∣ Ψ ⟩ = 0$ .

These two conditions are not silently identified. The extraction identity requires neither. Stationarity is used only in the relational-evolution clause.

Displayed formulas in this passage

En09-A@1#eq:constraint · line 271
$K = H_{C} \otimes I_{S} + I_{C} \otimes H_{S} .$
En09-A@1#eq:stationarity · line 276
$[K, ρ_{C S}] = 0.$
En09-A@1#eq:strong-constraint · line 281
$K ρ_{C S} = 0.$

Stationarity and the stronger constraint

Displayed formulas in this passage

Nearby in this section