Quantum Discord vs Entanglement

Classical vs quantum correlations in two-qubit mixed states

I(A:B) total
S(ρ_AB)
Concurrence C
Discord D
Classical J
Quantum mutual information: I(A:B) = S(ρ_A) + S(ρ_B) − S(ρ_AB). This splits into classical + quantum parts.
Quantum discord D(A|B) = I(A:B) − J(A|B), where J = max over measurements on B of classical mutual info. Discord can be nonzero even for separable (unentangled) states — quantum correlations beyond entanglement.
Werner states: ρ = (1−p)|Φ⁺⟩⟨Φ⁺| + p·I/4. Entangled for p < 2/3; discord > 0 for p < 1. Key insight: entanglement ⊂ discord — all entangled states have discord, but not vice versa.