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Let B_1,B_2 be balls in finite-dimensional real vector spaces E_1,E_2,centered around unit length vectors v_1,v_2 and not containing zero. An elementin the tensor product space E_1 \otimes E_2 is called B_1 \otimes B_2-separableif it is contained in the convex conic hull of elements of the form w_1 \otimesw_2, where w_1 \in B_1, w_2 \in B_2. We study the cone formed by the separableelements in E_1 \otimes E_2. We determine the largest faces of this cone via adescription of the extreme rays of the dual cone, i.e. the cone of thecorresponding positive linear maps. We compute the radius of the largest ballcentered around v_1 \otimes v_2 that consists of separable elements. As anapplication we obtain lower bounds on the radius of the largest ball ofseparable unnormalized states around the identity matrix for a multi-qubitsystem. These bounds are approximately 12% better than the best previouslyknown. Our results are extendible to the case where B_1,B_2 are solidellipsoids.

Entangled states close to the maximally mixed state