  The work deficit, as introduced by Jonathan Oppenheim \emph{et al}[Phys. Rev.
Lett. \textbf{89}, 180402 (2002)] is a good measure of the quantum correlations
in a state and provides a new standpoint for understanding quantum
non-locality. In this paper, we analytically evaluate the one-way information
deficit (OWID) for the Bell-diagonal states and a class of two-qubit states and
further give the geometry picture for OWID. The dynamic behavior of the OWID
under decoherence channel is investigated and it is shown that the OWID of some
classes of $X$ states is more robust against the decoherence than the
entanglement.
