nLab unital quantum channel

Idea

A quantum channel

$$chan \,\colon\, \mathscr{H}_1 \otimes \mathscr{H}^\ast_1 \longrightarrow \mathscr{H}_1 \otimes \mathscr{H}^\ast_1$$

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

In any operator-sum decomposition of the channel as

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

this means that not only

$$\underset{s}{\sum} \, E_s^\dagger \cdot E_s \;=\; id_{\mathscr{H}_1}$$

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

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

Related concepts

• unistochastic quantum channel

References

See most references on quantum channels.

• Christian Mendl, Unital Quantum Channels, talk (2007) [pdf]