The absolutely separable (resp. positive partial transpose) states remain separable (resp. PPT) under any global unitary operation. We present a compact form of the extreme points in the sets of absolutely separable states and PPT states in two-qubit and qubit-qudit systems. The results imply that each extreme point has at most three distinct eigenvalues. For a two-qubit system, we also quantify geometric probabilities of absolute separability. We establish a necessary and sufficient condition for determining extreme points of the set of absolutely PPT states in two-qutrit and qutrit-qudit systems, expressed as solvable linear equations. We also demonstrate that any extreme point in a qutrit-qudit system has at most seven distinct eigenvalues. We introduce the concept of robustness of nonabsolute separability. It quantifies the minimal amount by which a state needs to mix with other states such that the overall state is absolutely separable. We show that the robustness satisfies positivity, invariance under unitary transformation, monotonicity, and convexity, so it is a good measure within the resource theory of nonabsolute separability. Analytical expressions for this measure are given for pure states in an arbitrary system and rank-two mixed states in a two-qubit system. Furthermore, we extend the study of absolutely separable and PPT states to multipartite systems, proving that three-qubit absolutely separable states form a proper subset of three-qubit absolutely PPT states, with symmetry under subsystem permutations and stricter spectral constraints.

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• Quantum correlations in quantum information
• Quantum correlations, foundations & formalism
• Quantum information theory