  Entanglement negativity is a measure of mixed-state entanglement increasingly
used to investigate and characterize emerging quantum many-body phenomena,
including quantum criticality and topological order. We present two results for
the entanglement negativity: a disentangling theorem, which allows the use of
this entanglement measure as a means to detect whether a wave-function of three
subsystems $A$, $B$, and $C$ factorizes into a product state for parts $AB_1$
and $B_2C$; and a monogamy relation, which states that if $A$ is very entangled
with $B$, then $A$ cannot be simultaneaously very entangled also with $C$.
