Quantendiskord

Quantendiskord, known in English as quantum discord, is a measure of nonclassical correlations in a bipartite quantum system that extends beyond entanglement. It was introduced in the early 2000s by Ollivier and Zurek, and independently by Henderson and Vedral, to capture quantum correlations that can persist even in separable states. The concept has since become a standard topic in quantum information theory.

Formally, for a composite state ρ_AB, the total correlations are described by quantum mutual information I(A:B) = S(ρ_A) + S(ρ_B) − S(ρ_AB), where S is the von Neumann entropy. Classical correlations are defined via measurements on one subsystem, J(A|B) = S(ρ_A) − min_{Π^B} Σ_k p_k S(ρ_A|k), with Π^B a set of measurements on B and ρ_A|k the post-measurement states of A. Quantum discord is the difference D(A|B) = I(A:B) − J(A|B). D(A|B) is nonnegative and, crucially, can be nonzero even when ρ_AB is not entangled, highlighting nonclassical correlations beyond entanglement. The measure is generally asymmetric in its arguments: D(A|B) may differ from D(B|A).

Computation of discord involves an optimization over measurements and is tractable in special cases (e.g., two-qubit states), but can be challenging in general. Variants exist, such as geometric discord, which uses a distance-to-zero-discord set, and related measures like measurement-induced disturbance.

Quantum discord has been studied for its potential operational significance in tasks where quantum advantages arise without strong entanglement, including certain quantum computational models and experiments in optics and other platforms. Its interpretation and applicability continue to be active areas of research.