The One-Way Information Deficit and Geometry for a Class of Two-qubit States

The work deficit, as introduced by Jonathan Oppenheim \emph{et al}[Phys. Rev. Lett. $\mathbf{\text{89}}$, 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.