  The behavior of general nonclassical two-mode Gaussian states at a beam
splitter is investigated. Single-mode nonclassicality as well as two-mode
entanglement of both input and output states are analyzed suggesting their
suitable quantifiers. These quantifiers are derived from local and global
invariants of linear unitary two-mode transformations such that the sum of
input (or output) local nonclassicality measures and entanglement measure gives
a global invariant. This invariant quantifies the global nonclassicality
resource. Mutual transformations of local nonclassicalities and entanglement
induced by the beam splitter are analyzed considering incident noisy twin
beams, single-mode noisy squeezed vacuum states, and states encompassing both
squeezed states and twin beams. A rich tapestry of interesting nonclassical
output states is predicted.
