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Better versions of separability conditions for four mode optical fields, i.e.two beams with two modes of mutually orthogonal polarization are given. Ourconditions involve variances. Their meaning is intuitive and theirimplementation is feasible. Namely, if for a given quantum state the spread ofthe data around its mean value is smaller than the minimal spread predicted forthe set of separable states, then the given state is entangled. Our conditionsare formulated for standard quantum Stokes observables and normalized Stokesobservables and result to be more efficient that the previous conditions forfour mode optical fields involving variances. We test our conditions for brightsqueezed vacuum with (and without) induced non-gaussianity obtained by additionor subtraction of photons. Also we propose a practical experimental scheme ofhow to generate such states for an event-ready experiment.

Improved entanglement indicators for optical fields and its application  in the event-ready experiment for bright squeezed vacuum with induced  non-gaussianity