A Sensitive Quantumness Measure for One-Dimensional Continuous-Variable Systems

For one-dimensional continuous-variable quantum systems such as single-mode quantum optical systems, we give a quantification of the quantumness of such a system’s state, ρ, by introducing the measure of quantumness, Ξ, which works for all states, pure or mixed. Ξ is a measure which is universal, sensitive, monotonic, and unbounded. Ξ[ρ] yields a single positive value to quantify how nonclassical ρ is. Ξ employs phase space distributions to represent ρ and is a fixed function, Ξ[.], independent of the system, its environment or the type of state.