Complex potential/ observable

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I have an observable denoted by $C$, related to a complex potential $B$ by :

$$ C= \bar{B}B ,$$

where $B$ is a complex potential. I know that $ \left. C \right|_0 =C_0 $, a known constant, where the evaluation at $_0$ denotes an equilibrium \ reference state. From this, I can not make any conclusions on $\left. B \right|_0$, or $ \left. \bar{B} \right|_0$ can I ?

Thanks.