Quantum Discord vs Entanglement

Quantum discord captures quantum correlations beyond entanglement. A separable (unentangled) two-qubit state can still have nonzero quantum discord — meaning classical measurement disturbs the state. The Werner state ρ = p|Ψ⁻⟩⟨Ψ⁻| + (1−p)I/4 is entangled for p>1/3, but has discord for all p>0. Explore how discord and concurrence differ across state families.

Current state (Werner + noise):
p = 0.50

Concurrence (Entanglement):
C =

Quantum Discord D:
D =

Entanglement region: p > 1/3
Discord region: p > 0
Key insight: Separable states
(1/3 < p = 0) can have discord —
quantum correlations without
entanglement!

Geometric discord:
D_G = min_χ∈CC ‖ρ−χ‖²_F