Related papers: Cohomological framework for contextual quantum com…
We provide a cohomological framework for contextuality of quantum mechanics that is suited to describing contextuality as a resource in measurement-based quantum computation. This framework applies to the parity proofs first discussed by…
We describe a joint cohomological framework for measurement-based quantum computation (MBQC) and the corresponding contextuality proofs. The central object in this framework is an element in the second cohomology group of the chain complex…
We introduce an equivariant version of contextuality with respect to a symmetry group, which comes with natural applications to quantum theory. In the equivariant setting, we construct cohomology classes that can detect contextuality. This…
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…
Contextuality is a key feature of quantum mechanics that provides an important non-classical resource for quantum information and computation. Abramsky and Brandenburger used sheaf theory to give a general treatment of contextuality in…
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 provides a unifying paradigm for nonclassical aspects of quantum probabilities and resources of quantum information. Unfortunately, most forms of quantum contextuality remain experimentally unexplored due to the difficulty of…
We construct a topological space to study contextuality in quantum mechanics. The resulting space is a classifying space in the sense of algebraic topology. Cohomological invariants of our space correspond to physical quantities relevant to…
Contextuality is a defining feature that separates the quantum from the classical descriptions of physical systems. Within the marginal-scenario framework, noncontextual models are characterized by the existence of a single joint…
Inhomogeneities are introduced in loop quantum cosmology using regular lattice states, with a kinematical arena similar to that in homogeneous models considered earlier. The framework is intended to encapsulate crucial features of…
Okay, Roberts, Bartlett and Raussendorf recently introduced a new cohomological approach to contextuality in measurement based quantum computation. We give an abstract description of their obstruction and the algebraic structure it…
Contextuality is a fundamental property of quantum theory and a critical resource for quantum computation. Here, we experimentally observe the arguably cleanest form of contextuality in quantum theory [A. Cabello \emph{et al.}, Phys. Rev.…
We introduce a new mathematical framework for the probabilistic description of an experiment on a system of any type in terms of information representing this system initially. Based on the notions of an information state and a generalized…
We develop the contextual measurement model (CMM) which is used for clarification of the quantum foundations. This model matches with Bohr's views on the role of experimental contexts. CMM is based on contextual probability theory which is…
Quantum coherence is an essential ingredient in quantum information processing and plays a central role in emergent fields such as nanoscale thermodynamics and quantum biology. However, our understanding and quantitative characterization of…
These lecture notes cover 13 sessions and are presented as an e-print, intended to evolve over time. Quantum invariants do more than distinguish topological objects; they build bridges between topology, algebra, number theory and quantum…
Quantum contextuality, a fundamental feature distinguishing quantum theory from classical models, is investigated via algebraic and topological structures inherent in modular tensor categories. This work rigorously demonstrates that braid…
From an operational perspective, quantumness characterizes the exotic behavior in a physical process which cannot be explained with Newtonian physics. There are several widely used measures of quantumness, including coherence, discord, and…
We initiate the systematic study of experimental quantum physics from the perspective of computational complexity. To this end, we define the framework of quantum algorithmic measurements (QUALMs), a hybrid of black box quantum algorithms…
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…