AUTHOR=Fu Shuangshuang , Luo Shunlong , Zhang Yue TITLE=On Non-Convexity of the Nonclassicality Measure via Operator Ordering Sensitivity JOURNAL=Frontiers in Physics VOLUME=10 YEAR=2022 URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2022.955786 DOI=10.3389/fphy.2022.955786 ISSN=2296-424X ABSTRACT=

In quantum optics, nonclassicality in the sense of Glauber-Sudarshan is a valuable resource related to the quantum aspect of photons. A desirable and intuitive requirement for a consistent measure of nonclassicality is convexity: Classical mixing should not increase nonclassicality. We show that the recently introduced nonclassicality measure [Phys. Rev. Lett. 122, 080402 (2019)] is not convex. This nonclassicality measure is defined via operator ordering sensitivity, which is an interesting and significant probe (witness) of nonclassicality without convexity but can be intrinsically connected to the convex Wigner-Yanase skew information [Proc. Nat. Acad. Sci. United States 49, 910 (1963)] via the square root operation on quantum states. Motivated by the Wigner-Yanase skew information, we also propose a faithful measure of nonclassicality, although it cannot be readily computed, it is convex.