Photon-varied quantum states: Unified characterization

This paper introduces photon-varied quantum states (PVQSs), which generalize the nonclassical states obtained via photon addition or subtraction operations. We provide a unified characterization of PVQSs in terms of characteristic function, quasiprobability distribution, Fock representation, and Mandel Q parameter. In the special case of photon-varied Gaussian states (PVGSs), the characteristic functions and the quasiprobability distributions are found to be in a simple canonical product structure. Necessary and sufficient conditions for the negativity of the quasiprobability distributions are also obtained for PVGSs. The unified characterization enables the design and analysis of quantum systems that exploit the non-Gaussian properties of PVQSs.