Largest separable balls around the maximally mixed bipartite quantum state
Leonid Gurvits, Howard Barnum
Abstract
For finite-dimensional bipartite quantum systems, we find the exact size of the largest balls, in spectral lp norms for 1 p ∞, 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 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.
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