A general state of an m*n system is a classical-quantum state if and only if its associated left-correlation matrix has rank no larger than m-1. Based on this condition, a computable measure of quantum discord is presented, which coincides with the tight lower bound on the geometric measure of discord. Therefore such obtained tight lower bound fully captures the quantum correlation of a bipartite system, so it can be used as a measure of discord in its own right. Accordingly, a vanishing tight lower bound on the geometric discord is a necessary and sufficient condition for a state to be zero-discord

Keywords: classical-quantum states, left-correlation matrix, quantum discord, quantum correlation.

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