Eur. Phys. J. Plus (2021) 136: 464
https://doi.org/10.1140/epjp/s13360-021-01459-z

Regular Article

Entropy excesses as quantifiers of nonclassicality

¹ Beijing Academy of Quantum Information Sciences, 100193, Beijing, China
² State Key Laboratory of Mesoscopic Physics, Frontiers Science Center for Nano-optoelectronics, School of Physics, Peking University, 100871, Beijing, China
³ Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100190, Beijing, China
⁴ School of Mathematical Sciences, University of Chinese Academy of Sciences, 100049, Beijing, China

^b luosl@amt.ac.cn

Received: 1 December 2020
Accepted: 19 April 2021
Published online: 28 April 2021

Abstract

Any quantum state of a bosonic field can be described by a density operator on the system Hilbert space, or equivalently, by the corresponding Husimi function on the phase space. For the density operator, there is a family of quantum Tsallis entropies (including the von Neumann entropy as a particular instance) quantifying its uncertainty (mixedness), and for the Husimi function, there is a corresponding family of classical Tsallis entropies (including the Wehrl entropy as a particular instance) synthesizing its phase-space uncertainty. We propose to use the entropy excesses, i.e., the differences between the classical Tsallis entropies and the quantum Tsallis entropies, as quantifiers of nonclassicality of bosonic field states. We elaborate on this idea and highlight the entropy excess arising from the difference between the Wehrl (classical) entropy and the von Neumann (quantum) entropy as a significant indicator of nonclassicality. We further illustrate these nonclassicality quantifiers by several widely used states in quantum optics. This entropic approach to nonclassicality sheds light on the nature of nonclassicality from an information-theoretic perspective involving the heterodyne measurement.