  An important open problem in quantum information theory is the question of
the existence of NPT bound entanglement. In the past years, little progress has
been made, mainly because of the lack of mathematical tools to address the
problem. (i) In an attempt to overcome this, we show how the distillability
problem can be reformulated as a special instance of the separability problem,
for which a large number of tools and techniques are available. (ii) Building
up to this we also show how the problem can be formulated as a Schmidt number
problem. (iii) A numerical method for detecting distillability is presented and
strong evidence is given that all 1-copy undistillable Werner states are also
4-copy undistillable. (iv) The same method is used to estimate the volume of
distillable states, and the results suggest that bound entanglement is
primarily a phenomenon found in low dimensional quantum systems. (v) Finally, a
set of one parameter states is presented which we conjecture to exhibit all
forms of distillability.
