  A particularly interesting feature of nonrelativistic quantum mechanics is
the monogamy laws of entanglement. Although the monogamy relation has been
explored extensively in the last decade, it is still not clear to what extent a
given entanglement measure is monogamous. We give here a conjecture on the
amount of entanglement contained in the reduced states by observing all the
known related results at first. Consequently, we propose the monogamy power of
an entanglement measure and the polygamy power for its dual quantity, the
assisted entanglement, and show that both the monogamy power and the polygamy
power exist in any multipartite systems with any dimension, from which we
formalize exactly for the first time when an entanglement measure and an
assisted entanglement obey the monogamy relation and the polygamy relation
respectively in a unified way. In addition, we show that any entanglement
measure violates the polygamy relation, which is misstated in some recent
papers. Only the existence of monogamy power is conditioned on the conjecture,
all other results are strictly proved.
