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

Definition: Specified localized device

The complete device extension and boundary compatibility · lines 1234–1248

En05-C@1#eq:internaldevice

A specified device includes its complete global UCP action. A localized Kraus realization is one sufficient way to specify it:

T_{b} (a) = μ = 1 \sum^{m_{b}} V_{b, μ}^{*} a V_{b, μ}, V_{b, μ} \in A (b), μ \sum V_{b, μ}^{*} V_{b, μ} = 1.

A chosen Kraus family is realization data, not a canonical observable associated to the channel. Different Kraus families may specify the same global channel.

Displayed formulas in this passage

En05-C@1#eq:internaldevice · line 1237
$T_{b} (a) = μ = 1 \sum^{m_{b}} V_{b, μ}^{*} a V_{b, μ}, V_{b, μ} \in A (b), μ \sum V_{b, μ}^{*} V_{b, μ} = 1.$

Nearby in this section

proposition: Proposition: A regional channel does not determine its device
section: The complete device extension and boundary compatibility
section: The complete device extension and boundary compatibility
proposition: Proposition: Shared boundary data cannot be independently changed
section: The complete device extension and boundary compatibility