  Continuing the study of mixed-state entanglement in terms of
opposite-subsystem observables the measurement of one of which amounts to the
same as that of the other (so-called twins), begun in a recent article,
so-called strong twin events, which imply biorthogonal mixing of states, are
defined and studied. It is shown that for each mixed state there exists a
Schmidt canonical (super state vector) expansion in terms of Hermitian
operators, and that it can be the continuation of the mentioned biorthogonal
mixing due to strong twins. The case of weak twins and nonhermitian Schmidt
canonical expansion is also investigated. A necessary and sufficient condition
for the existence of nontrivial twins for separable states is derived.
