nLab unital quantum channel



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A quantum channel

chan: 1 1 * 1 1 * chan \,\colon\, \mathscr{H}_1 \otimes \mathscr{H}^\ast_1 \longrightarrow \mathscr{H}_1 \otimes \mathscr{H}^\ast_1

is called unital if it preserves the maximally mixed quantum state.

In any operator-sum decomposition of the channel as

chan:ρsE sρE s chan \;\colon\; \rho \;\mapsto\; \underset{s}{\sum} \, E_s \cdot \rho \cdot E_s^\dagger

this means that not only

sE s E s=id 1 \underset{s}{\sum} \, E_s^\dagger \cdot E_s \;=\; id_{\mathscr{H}_1}

(reflecting the preservation of the trace of density matrices) but also

sE sE s =id 2. \underset{s}{\sum} \, E_s \cdot E_s^\dagger \;=\; id_{\mathscr{H}_2} \,.


See most references on quantum channels.

Created on September 28, 2023 at 10:55:17. See the history of this page for a list of all contributions to it.