Title: Wehrl Entropy Based Quantification of Nonclassicality for Single Mode Quantum Optical States,
Abstract: Nonclassical states of a quantized light are described in terms of
Glauber-Sudarshan P distribution which is not a genuine classical probability
distribution. Despite several attempts, defining a uniform measure of
nonclassicality (NC) for the single mode quantum states of light is yet an open
task. In our previous work [Phys. Rev. A 95, 012330 (2017)] we have shown that
the existing well-known measures fail to quantify the NC of single mode states
that are generated under multiple NC-inducing operations. Recently, Ivan et.
al. [Quantum. Inf. Process. 11, 853 (2012)] have defined a measure of
non-Gaussian character of quantum optical states in terms of Wehrl entropy.
Here, we adopt this concept in the context of single mode NC. In this paper, we
propose a new quantification of NC for the single mode quantum states of light
as the difference between the total Wehrl entropy of the state and the maximum
Wehrl entropy arising due to its classical characteristics. This we achieve by
subtracting from its Wehrl entropy, the maximum Wehrl entropy attainable by any
classical state that has same randomness as measured in terms of von-Neumann
entropy. We obtain analytic expressions of NC for most of the states, in
particular, all pure states and Gaussian mixed states. However, the evaluation
of NC for the non-Gaussian mixed states is subject to extensive numerical
computation that lies beyond the scope of the current work. We show that, along
with the states generated under single NC-inducing operations, also for the
broader class of states that are generated under multiple NC-inducing
operations, our quantification enumerates the NC consistently.