Related papers: A comonadic view of simulation and quantum resourc…
A notion of morphism that is suitable for the sheaf-theoretic approach to contextuality is developed, resulting in a resource theory for contextuality. The key features involve using an underlying relation rather than a function between…
We employ the resource theory of generalized contextuality as a tool for analyzing the structure of prepare-and-measure scenarios. We argue that this framework simplifies proofs of quantum contextuality in complex scenarios and strengthens…
Quantum theory departs from classical physics in its treatment of correlations, most prominently through the phenomena of contextuality and nonlocality. Once regarded primarily as foundational curiosities, these effects are now understood…
Contextuality - the obstruction to describing quantum mechanics in a classical statistical way - has been proposed as a resource that powers quantum computing. The measurement-based model provides a concrete manifestation of contextuality…
We unify the resource-theoretic and the cohomological perspective on quantum contextuality. At the center of this unification stands the notion of the contextual fraction. For both symmetry and parity based contextuality proofs, we…
We develop a resource theory of contextuality within the framework of symmetric monoidal categories, extending recent simplicial approaches to quantum contextuality. Building on the theory of simplicial distributions, which integrates…
Resource theories constitute a powerful theoretical framework and a tool that captures, in an abstract structure, pragmatic aspects of the most varied theories and processes. For physical theories, while this framework deals directly with…
The sheaf theoretic description of non-locality and contextuality by Abramsky and Brandenburger sets the ground for a topological study of these peculiar features of quantum mechanics. This viewpoint has been recently developed thanks to…
Contextuality has been identified as a potential resource responsible for the quantum advantage in several tasks. It is then necessary to develop a resource-theoretic framework for contextuality, both in its standard and generalized forms.…
This chapter contains an exposition of the sheaf-theoretic framework for contextuality emphasising resource-theoretic aspects, as well as some original results on this topic. In particular, we consider functions that transform empirical…
In this thesis we use the language of sheaf theory in order to develop a deeper understanding of some of the fundamental differences - such as entanglement, contextuality and non-locality - between quantum and classical physics. We first…
Contextuality has been conjectured to be a super-classical resource for quantum computation, analogous to the role of non-locality as a super-classical resource for communication. We show that the presence of contextuality places a lower…
Resource theories can be used to formalize the quantification and manipulation of resources in quantum information processing such as entanglement, asymmetry and coherence of quantum states, and incompatibility of quantum measurements.…
We introduce novel schemes for quantum computing based on local measurements on entangled resource states. This work elaborates on the framework established in [Phys. Rev. Lett. 98, 220503 (2007), quant-ph/0609149]. Our method makes use of…
Contextuality, a generalization of non-locality, has been proposed as the resource that provides the computational speed-up for quantum computation. For universal quantum computation using qudits, of odd-prime dimension, contextuality has…
Homomorphisms between relational structures play a central role in finite model theory, constraint satisfaction and database theory. A central theme in quantum computation is to show how quantum resources can be used to gain advantage in…
We offer new methods for characterizing general closed and convex quantum resource theories, including dynamic ones, based on entropic concepts and operational tasks. We propose a resource-theoretic generalization of the quantum conditional…
Recent developments surrounding resource theories have shown that any quantum state or measurement resource, with respect to a convex (and compact) set of resourceless objects, provides an advantage in a tailored subchannel or state…
An empirical model is a generalization of a probability space. It consists of a simplicial complex of subsets of a class X of random variables such that each simplex has an associated probability distribution. The ensuing marginalizations…
In addition to the important role of contextuality in foundations of quantum theory, this intrinsically quantum property has been identified as a potential resource for quantum advantage in different tasks. It is thus of fundamental…