Largest separable balls around the maximally mixed bipartite quantum state

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