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We characterize the boundary of the convex compact set of absolutelyseparable states, referred as {\bf AS}, that cannot be transformed to entangledstates by global unitary operators, in $2\otimes d$ Hilbert space. However, weshow that the absolutely separable states of rank-$(2d-1)$ are extreme pointsof such sets. We then discuss conditions to examine if a given full-rankabsolutely separable state is an interior point or a boundary point of {\bfAS}. Moreover, we construct two-qubit absolutely separable states which areboundary points but not extreme points of {\bf AS} and prove the existence offull-rank extreme points of {\bf AS}. Properties of certain interior points arealso explored. We further show that by examining the boundary of the above set,it is possible to develop an algorithm to generate the absolutely separablestates which stay outside the maximal ball. By considering paradigmatic noisemodels, we find the amount of local noise which the input entangled states cansustain, so that the output states do not become absolutely separable.Interestingly, we report that with the decrease of entanglement of the pureinput state, critical depolarizing noise value, transferring an entangled stateto an absolutely separable one, increases, thereby showing advantages ofsharing nonmaximally entangled states. Furthermore, when the input two-qubitstates are Haar uniformly generated, we report a hierarchy among quantumchannels according to the generation of absolutely separable states.

Characterizing the boundary of the set of absolutely separable states and their generation via noisy environments