Exploring the optimal sensitivity of sum-variance nonseparability criteria for spin-1∕2systems

We report on experimental and theoretical studies on recently introduced entanglement measures which use a sum of spin-variance criteria for two spin-$1∕2$ particles. Three inequalities are explored which exhibit useful concatenating properties. They are each shown to have greater sensitivities than a Bell's measurement, while each requiring fewer measurements than a Bell's measurement to obtain. The simplest inequality, requiring just four measurements, is shown to be efficient at testing for entanglement in down-conversion sources which naturally exhibit maximally polarized noise. The most complex inequality, requiring just 12 measurements, is shown to have a sensitivity equal to that of the Peres separability criterion for maximally polarized and Werner noise. This increased sensitivity implies optimality of the measure.