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Quantum correlations characterized by quantum entanglement and quantumdiscord play important roles in many quantum information processing. We studythe relations among the entanglement of formation, concurrence, tangle, linearentropy based classical correlation and von Neumann entropy based classicalcorrelation. We present analytical formulae of linear entropy based classicalcorrelation for arbitrary $d\otimes 2$ quantum states and von Neumann entropybased classical correlation for arbitrary $2\otimes 2$ rank-2 quantum states.From the von Neumann entropy based classical correlation, we derive an explicitformula of quantum discord for arbitrary rank-2 two-qubit quantum states.

Analytical Expression of Quantum Discord for Rank-2 Two-qubit States