  A density-matrix method for the study of tagged states of neutral B mesons
with arbitrary coherence properties is applied to several examples, including
$e^+ e^-$ production both at and above the $\Upsilon(4S)$ resonance, and
hadronic production. In the absence of coherence the only term modulating the
exponential decay of a neutral B meson behaves as $\cos \Delta m t$, while a
$\sin \Delta m t$ modulation is a signal of partial or full coherence. Decays
to CP eigenstates are needed to fully specify the density matrix. We relate
these results to more familiar expressions for the cases of the $\Upsilon(4S)$
and incoherent production.
