Universal Quantumness Measure for One-Dimensional Continuous-Variable Systems

Ole Steuernagel^1*

¹1 Institute of Photonics Technologies, National Tsing Hua University, Hsinchu, Taiwan

* Presenter:Ole Steuernagel, email:librarole@gmail.com

A bewildering number of different approaches have been devised to answer this seemingly straightforward question: Is this physical system in a classical state or in a quantum state; and if quantum, how to quantify how nonclassical this state is? No consensus has emerged even for continuous quantum systems in one-dimension only. Indeed, a recent review [F. Fröwis, et al., Macroscopic quantum states: Measures, fragility, and implementations, Rev. Mod. Phys. 90, 025004 (2018)] concluded: “already the precise meaning of these and similar words is unclear and disputed and also because they are heavily loaded with emotions and prejudice.” For one-dimensional continuous-variable quantum systems such as single-mode quantum optical systems, we settle the question of the quantification of the quantumness of such a system’s state, ρ̂, by introducing the measure of quantumness, Ξ, which works for all states, pure or mixed. Ξ is the first measure which is universal, discriminating, monotonic, and unbounded. Ξ[ρ̂] yields a single positive value to quantify how nonclassical ρ̂ is. Ξ employs phase space distributions to represent ρ̂ and is a fixed functional, Ξ[·], independent of the system, its environment or the type of state.

Keywords: quantum versus classical physics, macroscopic superpositions , measure of quantumness