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.