Resource Theory of Non-absolute Separability

Abstract: We develop a resource theory for non-absolutely separable states (non-AS) in which absolutely separable states (AS) that cannot be entangled by any global unitaries are recognised as free states and any convex mixture of global unitary operations can be performed without incurring any costs. We employ two approaches to quantify non-absolute separability (NAS) -- one based on distance measures and the other one through the use of a witness operator. We prove that both the NAS measures obey all the conditions which should be followed by a ``good'' NAS measure. We demonstrate that NAS content is equal and maximal in all pure states for a fixed dimension. We then establish a connection between the distance-based NAS measure and the entanglement quantifier. We illustrate our results with a class of non-AS states, namely Werner states.