Journal of Physics A, Mathematical and Theoretical vol:41 issue:6 pages:-
We propose a simple test of quantumness which can decide whether for a given set of accessible experimental data the classical model is insufficient. Take two observables A, B such that for all states. their mean values satisfy 0 <= <psi |A | psi > <= <psi | B | psi > <= 1. If there exists a state phi such that the second moments fulfill the inequality <phi | A(2)| phi > > <phi| B-2| phi > then the system cannot be described by a classical probabilistic scheme. An example of an optimal triple ( A, B, f) in the case of a qubit is given.