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.

玻色子场的任何量子态都可以由希尔伯特系统上的密度算符来描述，或者等效地由相空间上的相应Husimi函数来描述。对于密度算符，有一个量子Tsallis熵家族（包括von Neumann熵作为一个特定实例），以量化其不确定性（混合性）；对于Husimi函数，有一个相应的经典Tsallis熵家族（包括Wehrl熵）合成其相空间不确定性。我们建议使用熵超额（即经典Tsallis熵和量子Tsallis熵之间的差）作为Bosonic场态非经典性的量词。我们详细阐述了这种想法，并强调了由Wehrl（经典）熵和von Neumann（量子）熵之间的差异引起的熵超额，这是非经典性的重要指标。我们通过量子光学中几种广泛使用的状态进一步说明了这些非经典性量词。从涉及外差测量的信息理论观点来看，这种对非经典性的熵方法揭示了非经典性的本质。