Identifying the classical-quantum divide and quantifying nonclassicality are fundamental issues in quantum exploration. By use of the Wigner-Yanase skew information [Proc. Nat. Acad. Sci. USA, 49, 910 (1963)], which synthesizes the noncommutativity between quantum states and observables, we introduce a simple yet effective measure of nonclassicality for any bosonic field state. This is achieved by considering measurement of the non-Hermitian annihilation operator from an information-theoretic perspective. This measure, apart from capturing the idea of nonclassicality as quantum uncertainty in a succinct way, is mathematically computable and physically intuitive. We investigate its fundamental properties, and illustrate its physical applications in quantifying nonclassicality of quantum states. We compare it with various existent measures of nonclassicality and illustrate its merits. A related measure of classicality, which is in some sense dual to nonclassicality, is also introduced. This pair of (classicality, nonclassicality) sheds novel insights into the classical-quantum interplay.
The research interest of Professor Shunlong Luo includes probability and statistics, quantum theory, information theory. He has published about 50 papers in mathematics and about 60 papers in physics. He is the director of the Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and the vice-president of Beijing Mathematical Society.