Quantification of nonclassicality

To quantify single-mode nonclassicality, we start from an operational approach. A positive semidefinite observable is introduced to describe a measurement setup. The quantification is based on the negativity of the normally ordered version of this observable. Perfect operational quantumness corresponds to the quantum-noise-free measurement of the chosen observable. Surprisingly, even moderately squeezed states may exhibit perfect quantumness for a properly designed measurement. The quantification is also considered from an axiomatic viewpoint, based on the algebraic structure of the quantum states and the quantum superposition principle. Basic conclusions from both approaches are consistent with this fundamental principle of the quantum world.

Figure 1

Scheme for QNF measurement with moderate squeezing. The interaction on the red sideband is stronger than on the blue one, $|{\Omega }_{\mathrm{r}}|>|{\Omega }_{\mathrm{b}}|$.