Resource Theory of Non-absolute Separability

TL;DR

This paper introduces a resource theory for non-absolutely separable states, defining free states and quantifying non-absolute separability using distance measures and witness operators, with applications to Werner states.

Contribution

It develops a novel resource theory for non-absolutely separable states and proposes two methods to quantify non-absolute separability, linking it to entanglement measures.

Findings

NAS measures satisfy all criteria for a good measure

NAS content is maximal in all pure states for fixed dimension

Distance-based NAS measure relates to entanglement quantifiers

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.