Abstract
Quantum discord goes beyond entanglement and exists in a wide range of quantum states that may be separable, playing a crucial role in quantum information tasks. In this paper, we firstly proposed a zero-discord criterion for two-qubit system based on the partial transposition of density matrix, and then extended it to the qubit-qudit system. By detailed examples we demonstrate the effectiveness of these criteria in detecting discord. Moreover, we provide an analytical lower bound of geometric quantum discord(GQD) using eigenvalue vectors of density matrix. Finally, we presented a one-way work deficit lower bound based on our lower bound of GQD.