  Distinguishability and predictability are part of complementarity relations
which apply to two different kinds of interference experiments, with and
without a path-detector, respectively. In [Opt. Comm. 179, 337 (2000)], Englert
and Bergou pointed out the possible connection between distinguishability,
predictability, and entanglement. They even conjectured that an entanglement
measure was hidden between the measures of distinguishability and
predictability. Here, we push forward this conjecture. We start defining a new
entropic distinguishability measure and suggesting an entanglement measure as
the difference between this entropic distinguishability and an entropic
predictability measure already defined in the literature. Besides, we prove
that it is possible to define an entanglement monotone from the largest value
of the distinguishability and the corresponding predictability, provided that
the predictability satisfy the criteria already established in the literature.
Thus, this result formally connects an entanglement monotone with
distinguishability and the corresponding predictability, without appealing to
specific measures.
