14 citations · 60 across the 26 of their papers we have counts for
10 papers · 1 filter
Vertex-transitive quantum graphs
Mac Hayes, Trevor Jess, Andre Kornell +1
We define a quantum graph to be vertex-transitive if the join of its automorphism group is the maximum quantum relation on its quantum vertex set, in direct analogy with the classi…
The quantum Ramsey numbers
Andrew Allen, Andre Kornell
Operator systems of matrices can be viewed as quantum analogues of finite graphs. This analogy suggests many natural combinatorial questions in linear algebra. We determine the qua…
Characterizations of homomorphisms among unital completely positive maps
Andre Kornell
We prove that a unital completely positive map between finite-dimensional C*-algebras is a homomorphism if and only if it is completely entropy-nonincreasing, where the relevant no…
A category of quantum posets
Andre Kornell, Bert Lindenhovius, Michael Mislove
We investigate a category of quantum posets that generalizes the category of posets and monotone functions. Up to equivalence, its objects are hereditarily atomic von Neumann algeb…
Discrete quantum structures
Andre Kornell
A majority of established quantum generalizations of discrete structures are shown to be instances of a single quantum generalization. In particular, the quantum graphs of Duan, Se…
Quantum extensions of ordinary maps
Andre Kornell
We define a loop to be quantum nullhomotopic if and only if it admits a nonempty quantum set of extensions to the unit disk. We show that the canonical loop in the unit circle is n…
Quantum sets
Andre Kornell
A quantum set is defined to be simply a set of nonzero finite-dimensional Hilbert spaces. Together with binary relations, essentially the quantum relations of Weaver, quantum sets…
V*-algebras
Andre Kornell
What is the correct noncommutative generalization of the functor for locally compact Hausdorff having a countable basis? Making the ansatz $K(\e…
Quantum Collections
Andre Kornell
We develop the viewpoint that the opposite of the category of W*-algebras and unital normal *-homomorphisms is analogous to the category of sets and functions. For each pair of W*-…
Quantum Functions
Andre Kornell
Weaver has recently defined the notion of a quantum relation on a von Neumann algebra. We demonstrate that the corresponding notion of a quantum function between two von Neumann al…