Quantum Discord — Geometric Measure

Quantum Discord D

Entanglement (Concurrence)

Classical Correlation

Mutual Information

State Parameters

Two-qubit X-state: ρ = [[a,0,0,z],[0,b,w,0],[0,w*,b,0],[z*,0,0,a]]

Parameter a 0.25 Off-diagonal |z| 0.3 Mixing |w| 0.1 Phase φ (z = |z|e^{iφ}) 0.0π

Correlation Measures

Discord D (geometric)—

Concurrence C—

Mutual Info I(A:B)—

Classical corr. J—

Entangled?—

Has Discord?—

About

Quantum discord (Ollivier & Zurek 2001, Henderson & Vedral 2001) captures quantum correlations beyond entanglement. D = I(A:B) − J(A|B), where J is the maximum classical correlation over measurements on B. Separable states can have non-zero discord. Geometric discord = min distance to zero-discord states. Relevant for quantum computation without entanglement.