Nonclassicality versus entanglement in a noncommutative space

In a setting of noncommutative space with minimal length we confirm the general assertion that the more nonclassical an input state for a beam splitter is, the more entangled its output state becomes. By analysing various nonclassical properties we find that the odd Schr\"odinger cat states are more nonclassical than the even Schr\"odinger cat states, hence producing more entanglement, which in turn are more nonclassical than coherent states. Both the nonclassicality and the entanglement can be enhanced by increasing the noncommutativity of the underlying space. In addition we find as a by-product some rare explicit minimum uncertainty quadrature and number squeezed states, i.e. ideal squeezed states.
Comment: 15 pages, 7 figures