Direct observation of any two-point quantum correlation function

Understand

The existence of noncompatible observables in quantum theory makes a direct operational interpretation of two-point correlation functions problematic.

• Here we challenge such a view by explicitly constructing a measuring scheme that, independently of the input state $\rho$ and observables $A$ and $B$, performs an unbiased optimal estimation of the two-point correlation function $\operatorname{Tr}[A \ \rho \ B]$.
• This shows that, also in quantum theory, two-point correlation functions are as operational as any other expectation value.
• A very simple probabilistic implementation of our proposal is presented.