  The primary goal of entanglement theory is to determine convertibility
conditions for two quantum states. Up until now, this has always been done with
the use of entanglement monotones. With the exception of the negativity, such
quantities tend to be rather uncomputable. We instead promote the idea of
conversion witnesses in this paper. A conversion witness is a function on pairs
of states and whose value determines whether a state can be converted into
another. We construct a conversion witness that can be efficiently computed for
arbitrary states in systems of any size. This conversion witness is always
better than the negativity at detecting when two entangled states are not
interconvertible. Furthermore, when considering states of two-qubit systems,
this new conversion witness is sometimes better than the entanglement of
formation. This shows that the study of conversion witness is in fact useful,
and may have applications in resource theories beyond that of entanglement.
