Preparational Uncertainty Relations for $N$ Continuous Variables

Understand

A smooth function of the second moments of $N$ continuous variables gives rise to an uncertainty relation if it is bounded from below.

• We present a method to systematically derive such bounds by generalizing an approach applied previously to a single continuous variable.
• New uncertainty relations are obtained for multi-partite systems which allow one to distinguish entangled from separable states.
• We also investigate the geometry of the "uncertainty region" in the $N(2N+1)$-dimensional space of moments.