For a given density operator

$\varrho = \sum | \phi _ { k } \rangle \left\langle \phi _ { k } |\right.$

Assuming it normalized (convex) implies

$\varrho = \sum p _ { k } \frac { | \phi _ { k } \rangle \left\langle \phi _ { k } | \right. } { \left\langle \phi _ { k } | \phi _ { k } \right\rangle }$

In addition, if we assume this decomposition is optimal, then we can define a function that is related to this state $\varrho$ by

$C _ { \Theta } ( \varrho ) = \sum p _ { k } C _ { \Theta } \left( \frac { | \phi _ { k } \rangle \left\langle \phi _ { k } | \right. } { \left\langle \phi _ { k …