Quantum correlation

A quantum correlation is a statistical relation among observables of a composite quantum system. For local observables $A$ and $B$, a useful diagnostic is $⟨A\otimes B⟩-⟨A\otimes I⟩⟨I\otimes B⟩$. Product states make this expression vanish for every pair of local observables.

Not every correlation in a quantum state is quantum entanglement. The separable mixture $[|00⟩⟨00|+|11⟩⟨11|]/2$ gives perfectly correlated computational-basis outcomes but has no entanglement. The pure Bell state $|{\Phi }^{+}⟩$ has the same outcomes in that basis while retaining coherent relative-phase information detectable in complementary bases. The measurement choices therefore matter when characterizing the kind of correlation present.