  We study the coherent dynamics of two interacting particles in a quantum
double-well and show that the Shannon entropy can be a definitive signature of
entanglement as an alternative to concur- rence, a connection not reported
previously. This physical model, involving tunneling and contact interaction,
is akin to the Hubbard model which explains the physics of interacting
particles in peri- odic potentials. We show that an interplay between tunneling
and contact interaction produces Bell like eigenstates ensuring thereby that
the concurrence and the Shannon entropy, two quantities with vastly different
physical interpretations, develop the same time dependence. Our result, applied
to three experimentally realized physical models works for both spatial and
spin degrees of freedom and is significant as it provides a novel measure of
entanglement applicable to many systems currently being explored for scalable
quantum computation.
