  To our knowledge, all known bipartite entanglement measures are symmetric
under exchange of subsystems. We ask if an entanglement measure that is not
symmetric can exist. A related question is if there is a state that cannot be
swapped by means of LOCC. We show, that in general one cannot swap states by
LOCC. This allows to construct nonsymmetric measure of entanglement, and a
parameter that reports asymmetry of entanglement contents of quantum state. We
propose asymptotic measure of asymmetry of entanglement, and show that states
for which it is nonzero, contain necessarily bound entanglement.
