Figure 1
From: Negativity vs. purity and entropy in witnessing entanglement
(Top) Scatterplots of \(S_{2}(A|B)\) vs \(S_{1}(A|B)\) and respective purity histograms for \(10^{6}\) 2-quDit systems for \(D=(2,3,5,8,10)\) with each plot labeled \(2\otimes 2\), \(3\otimes 3\), \(5\otimes 5\), \(8\otimes 8\),and \(10\otimes 10\), respectively. The light orange scatterplots are from the fully uniform ensemble (abbreviated UE) while the blue scatterplots are from the ensemble uniform with respect to purity (abbreviated UP). The inset histograms are of the joint purity of the fully uniform ensemble). The red dotted line in each plot is where \(S_{1}(A|B)=S_{2}(A|B)\). The set of all \(D\otimes D\) pure states is within the green serrated blade region in the lower left quadrant (or is only a single curve for \(2\otimes 2\)), while the set of all \(D\otimes D\) states with maximally mixed marginals corresponds to the large magenta serrated blade spanning three quadrants of the plot. The regions enclosed between the two blades also correspond to valid density matrices. (Bottom) This table gives the percentages of the total number of generated states whose entanglement was witnessed with the function in the first column.
