quantumness, quantum witness, Science & Technology, Physical Sciences, Physics, Multidisciplinary, Physics, Mathematical, Physics, 2 SUPERCONDUCTING QUBITS, HIDDEN VARIABLES, STATES, 01 Mathematical Sciences, 02 Physical Sciences, Mathematical Physics
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.