  For finite-dimensional bipartite quantum systems, we find the exact size of
the largest balls, in spectral $l_p$ norms for $1 \le p \le \infty$, of
separable (unentangled) matrices around the identity matrix. This implies a
simple and intutively meaningful geometrical sufficient condition for
separability of bipartite density matrices: that their purity $\tr \rho^2$ not
be too large. Theoretical and experimental applications of these results
include algorithmic problems such as computing whether or not a state is
entangled, and practical ones such as obtaining information about the existence
or nature of entanglement in states reached by NMR quantum computation
implementations or other experimental situations.
