  It is well known that for pure states the relative entropy of entanglement is
equal to the reduced entropy, and the closest separable state is explicitly
known as well. The same holds for Renyi relative entropy per recent results. We
ask the same question for a quasi-relative entropy of entanglement, which is an
entanglement measure defined as the minimum distance to the set of separable
state, when the distance is measured by the quasi-relative entropy. First, we
consider a maximally entangled state, and show that the closest separable state
is the same for any quasi-relative entropy as for the relative entropy of
entanglement. Then, we show that this also holds for a certain class of
functions and any pure state. And at last, we consider any pure state on two
qubit systems and a large class of operator convex function. For these, we find
the closest separable state, which may not be the same one as for the relative
entropy of entanglement.
