Quantum Discord
Discord captures quantum correlations that survive even in some separable states, going beyond entanglement.
Two classically equal ways to write correlation
Classically, the mutual information between two variables has two equivalent expressions: one from joint and marginal entropies, and one built from conditional entropy defined via measurement. Quantum mechanically these two expressions can disagree, because measuring one subsystem disturbs it. The quantum discord is the difference between the two, minimized over local measurements on one side. It quantifies correlations that a local measurement inevitably destroys.
Definition
For a state rho_AB, let I(A:B) = S(rho_A) + S(rho_B) - S(rho_AB) be the total mutual information. Let J(A:B) be the classical correlation obtained by measuring B optimally and taking the resulting information about A. Discord is D = I - J, minimized over B measurements. It is nonnegative and vanishes only for states that are classical with respect to B, i.e. diagonal in some local basis on B.
Beyond entanglement
Every entangled state has positive discord, but the converse fails: there are separable, non-entangled states with nonzero discord. These carry genuinely quantum correlations even though no entanglement is present. Discord thus draws a finer line than the entanglement/separable boundary, identifying a broader class of nonclassical states.
- Zero discord: classically correlated (diagonal in a local basis)
- Positive discord, separable: nonclassical but not entangled
- Entangled: always positive discord
Significance and caveats
Discord has been linked to speedups in certain mixed-state computation models where entanglement is negligible, suggesting quantum advantage may not always require entanglement. It also appears in thermodynamic and metrological settings. The caveats are real: computing discord requires an optimization over measurements that is hard in general, its operational meaning is more subtle than entanglement's, and it is asymmetric between the two subsystems. It remains a useful lens on where the quantum-classical boundary actually lies.