  We investigate the properties of three entanglement measures that quantify
the statistical distinguishability of a given state with the closest
disentangled state that has the same reductions as the primary state. In
particular, we concentrate on the relative entropy of entanglement with
reversed entries. We show that this quantity is an entanglement monotone which
is strongly additive, thereby demonstrating that monotonicity under local
quantum operations and strong additivity are compatible in principle. In
accordance with the presented statistical interpretation which is provided,
this entanglement monotone, however, has the property that it diverges on pure
states, with the consequence that it cannot distinguish the degree of
entanglement of different pure states. We also prove that the relative entropy
of entanglement with respect to the set of disentangled states that have
identical reductions to the primary state is an entanglement monotone. We
finally investigate the trace-norm measure and demonstrate that it is also a
proper entanglement monotone.
