Coherence and contextuality as quantum resources

TL;DR

This thesis develops a graph-theoretic framework linking quantum coherence and contextuality, revealing new witnesses and advantages in quantum interrogation, advancing foundational understanding and potential applications.

Contribution

It introduces a novel graph-theoretic approach connecting coherence and contextuality, and demonstrates their practical advantages in quantum tasks.

Findings

Established a formal connection between coherence and contextuality inequalities.

Developed an infinite family of coherence witnesses requiring specific quantum state dimensions.

Proved contextual advantage in quantum interrogation.

Abstract

In this thesis, we explore the intersection of two fundamental subfields of quantum information theory: quantum coherence and contextuality. Despite their apparent differences, both areas address key issues relevant to the foundations and applications of quantum theory. By developing a novel graph-theoretic approach, extending a framework recently introduced by Galv\~ao and Brod (Phys. Rev. A 101, 062110, 2020), we establish a formal connection between inequality-based witnesses of quantum coherence and noncontextuality inequalities. Our key contributions include: the development of a graph-theoretic framework for generating coherence and contextuality witnesses; a formal mapping between the inequalities that follows from the work by Galv\~ao and Brod to existing noncontextuality inequalities; the conceptualization of a relational form of quantum coherence; a proof of contextual advantage for the task of quantum interrogation; and the discovery of an infinite family of coherence witnesses that also require quantum states in Hilbert spaces of specific dimensions.