Direct observation of any two-point quantum correlation function

TL;DR

This paper presents a measurement scheme that allows direct, unbiased estimation of two-point quantum correlation functions, demonstrating their operational accessibility similar to other expectation values.

Contribution

The authors construct a universal measurement scheme for directly estimating two-point correlation functions in quantum systems, overcoming previous interpretational challenges.

Findings

The scheme provides unbiased estimates regardless of input state and observables.

It demonstrates the operational equivalence of two-point correlations to other expectation values.

A simple probabilistic implementation of the measurement scheme is proposed.

Abstract

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.