We propose a three-qubit partially entangled set of states as a shared resource for optimal and faithful quantum information processing. We show that our states always violate the Svetlichny inequality, which is a Bell-type inequality whose violation is a sufficient condition for the confirmation of genuine three-qubit nonlocality. Although our states can be physically realized from the generalized Greenberger-Horne-Zeilinger (GGHZ) states using a simple quantum circuit, the nonlocal properties of the set are quite different from the GGHZ states. Instead, they are similar to the maximal slice (MS) states, even though our states are not locally equivalent to the MS states. Unlike other two- and three-qubit partially entangled states, quantum teleportation using our states results in faithful transmission of information with unit probability and unit fidelity by performing only standard measurements for the sender, controller, and receiver. We further demonstrate that dense coding also leads to the deterministic transfer of a maximum number of bits from the sender to the receiver. We also introduce witness operators able to experimentally detect the family of states introduced. This work highlights the importance of both the local as well as nonlocal aspects of quantum correlations in multiqubit systems. © 2013 American Physical Society.