  A crucial goal of quantum information is to find new ways to exploit the
properties of quantum devices as resources. One of the prominent properties of
quantum devices of particular interest is their negativity in quasi-probability
representations, intensively studied in foundational and practical
investigations. In this article, we introduce the concept of Absolute
Negativity to characterise the negativity of sets of quantum devices in a
basis-independent way. Moreover, we provide a resource theory for our
relational notion of Absolute Negativity, which applies to sets of quantum
state-measurement pairs. Additionally, we determine a complete hierarchy of
upper bounds for resource measures, which allows for estimating the resources
of a set of devices. We demonstrate operational interpretations of our resource
theory for communication and output-estimation advantages over
state-measurement pairs with a classical probability representation.
Furthermore, we illustrate the newly introduced concepts with an exhaustive
analysis of a simple case of four qubit state-measurement pairs. Finally, we
outline possible generalisations, applications and open questions.
