Moments of nonclassicality quasiprobabilities

A method is introduced for the verification of nonclassicality in terms of moments of nonclassicality quasiprobability distributions. The latter are easily obtained from experimental data and will be denoted as nonclassicality moments. Their relation to normally-ordered moments is derived, which enables us to verify nonclassicality by using well established criteria. Alternatively, nonclassicality criteria are directly formulated in terms of nonclassicality moments. The latter converge in proper limits to the usually used criteria, as is illustrated for squeezing and sub-Poissonian photon statistics. Our theory also yields expectation values of any observable in terms of nonclassicality moments.Comment: 6 pages, 3 figure

Nonclassicality filters and quasiprobabilities

Necessary and sufficient conditions for the nonclassicality of bosonic quantum states are formulated by introducing nonclassicality filters and nonclassicality quasiprobability distributions. Regular quasiprobabilities are constructed from characteristic functions which can be directly sampled by balanced homodyne detection. Their negativities uncover the nonclassical effects of general quantum states. The method is illustrated by visualizing the nonclassical nature of a squeezed state.Comment: Significantly revised version, more emphasis on practical applicatio

Conservation relation of nonclassicality and entanglement for Gaussian states in a beam-splitter

We study the relation between single-mode nonclassicality and two-mode entanglement in a beam-splitter. We show that not all of the nonclassicality (entanglement potential) is transformed into two-mode entanglement for an incident single-mode light. Some of the entanglement potential remains as single-mode nonclassicality in the two entangled output modes. Two-mode entanglement generated in the process can be equivalently quantified as the increase in the minimum uncertainty widths (or decrease in the squeezing) of the output states compared to the input states. We use the nonclassical depth and logarithmic negativity as single-mode nonclassicality and entanglement measures, respectively. We realize that a conservation relation between the two quantities can be adopted for Gaussian states, if one works in terms of uncertainty width. This conservation relation is extended to many sets of beam-splitters.Comment: 10 pages, 8 figure