Related papers: The Quantum Monad on Relational Structures
Bell non-locality is a fundamental feature of quantum mechanics whereby measurements performed on "spatially separated" quantum systems can exhibit correlations that cannot be understood as revealing predetermined values. This is a special…
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…
Contextuality is a non-classical behaviour that can be exhibited by quantum systems. It is increasingly studied for its relationship to quantum-over-classical advantages in informatic tasks. To date, it has largely been studied in…
Combinatorial games are widely used in finite model theory, constraint satisfaction, modal logic and concurrency theory to characterize logical equivalences between structures. In particular, Ehrenfeucht-Fraisse games, pebble games, and…
Game comonads offer a categorical view of a number of model-comparison games central to model theory, such as pebble and Ehrenfeucht-Fra\"iss\'e games. Remarkably, the categories of coalgebras for these comonads capture preservation of…
We establish a strong link between two apparently unrelated topics: the study of conflicting information in the formal framework of valuation algebras, and the phenomena of non-locality and contextuality. In particular, we show that these…
Game theory is a well established branch of mathematics whose formalism has a vast range of applications from the social sciences, biology, to economics. Motivated by quantum information science, there has been a leap in the formulation of…
In previous work, Abramsky, Dawar and Wang (LiCS 2017) and Abramsky and Shah (CSL 2018) have shown how a range of model comparison games which play a central role in finite model theory, including Ehrenfeucht-Fraisse, pebbling, and…
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…
We show a general method of compiling any $k$-prover non-local game into a single-prover interactive game maintaining the same (quantum) completeness and (classical) soundness guarantees (up to negligible additive factors in a security…
Contextuality can be understood as the impossibility to construct a globally consistent description of a model even if there is local agreement. In particular, quantum models present this property. We can describe contextuality with the…
The quantum mechanics is proved to admit no hidden-variable in 1960s, which means the quantum systems are contextual. Revealing the mathematical structure of quantum mechanics is a significant task. We develop the approach of partial…
We use monads to relax the atomicity requirement for data in a database. Depending on the choice of monad, the database fields may contain generalized values such as lists or sets of values, or they may contain exceptions such as various…
Using the simulation paradigm in information theory, we define notions of quantum hypergraph homomorphisms and quantum hypergraph isomorphisms, and show that they constitute partial orders and equivalence relations, respectively.…
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…
Contextuality in quantum physics provides a key resource for quantum information and computation. The topological approach in [Abramsky and Brandenburger, New J. Phys., 2011, Abramsky et al., CSL 2015, 2015] characterizes contextuality as…
Quantum contextual sets have been recognized as resources for universal quantum computation, quantum steering and quantum communication. Therefore, we focus on engineering the sets that support those resources and on determining their…
Models of a phenomenon are often developed by examining it under different experimental conditions, or measurement contexts. The resultant probabilistic models assume that the underlying random variables, which define a measurable set of…
The quantum mechanical formalism doesn't support our intuition, nor does it elucidate the key concepts that govern the behaviour of the entities that are subject to the laws of quantum physics. The arrays of complex numbers are kin to the…
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.…