Figure 1

The simplices of symmetric states for the cases of (α,β), α=β=1,2,3, respectively. The equilateral triangle has been marked with contour lines, on each of which one of the parameters is constant. The set of PPT states is indicated by the grey line segment in the top graph, the shaded area of the (2,2) triangle, and the filled polygon which obscures the μ3(3,3)=1 vertex in the (3,3) tetrahedral space. In all graphs only the projector of highest spin is within the PPT set. For all three cases, the set of all possible down-conversion states is a curve ending at the boundary of the PPT set, shown by the solid black line for the (1,1) space, and by the dotted curves for the (2,2) and (3,3) spaces. The position of the state on the curve is determined by the parameter ξ=(1−η)tanh(κt).Reuse & Permissions

Figure 2

Lower bounds to the relative entropy of entanglement for down-conversion states with initial average photon numbers of 0.5 (solid), 1 (dashed), and 3 (dotted line) subject to loss, evaluating the sum of Eq. (21) up to a truncation of α, β⩽5. This gives a good approximation to the total entanglement for average photon numbers before loss up to about 3.Reuse & Permissions