Resource theory of Absolute Negativity

Abstract

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.