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

Abstract

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, {\rho}, by introducing the measure of quantumness, {\Xi}, which works for all states, pure or mixed. {\Xi} is a measure which is universal, sensitive, monotonic, and unbounded. {\Xi}[{\rho}] yields a single positive value to quantify how nonclassical {\rho} is. {\Xi} employs phase space distributions to represent {\rho} and is a fixed function, {\Xi}[.], independent of the system, its environment or the type of state.