14 citations · 60 across the 26 of their papers we have counts for
27 papers
Localizing quantum information
Fahimeh Bayeh, Andre Kornell
The idea that information can be localized is pervasive in physics. In thermodynamics, entropy flows from one reservoir to another, and in quantum gravity, the entropy content of s…
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…
Quantum graphs of homomorphisms
Andre Kornell, Bert Lindenhovius
We introduce a category of quantum graphs, whose definition is motivated entirely from noncommutative geometry. For all quantum graphs and in $\mathsf{qGph}…
A new characterization of Kac-type discrete quantum groups
Alexandru Chirvasitu, Andre Kornell
We obtain two related characterizations of discrete quantum groups and discrete quantum groups of Kac type as allegorical group objects in the symmetric monoidal dagger category of…
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…
The category of topological spaces and open maps does not have products
Guram Bezhanishvili, Andre Kornell
We prove that the category of topological spaces and open maps does not have binary products, thus resolving the Esakia problem in the negative. We also prove that the categories o…
Categories of quantum cpos
Andre Kornell, Bert Lindenhovius, Michael Mislove
This paper unites two research lines. The first involves finding categorical models of quantum programming languages and their type systems. The second line concerns the program of…
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…
Some improvements to product formula circuits for Hamiltonian simulation
Andre Kornell, Peter Selinger
We provide three improvements to the product formula implementation of the ground state energy estimation algorithm via Trotter-Suzuki decomposition. These consist of smaller circu…
On the structure of modal and tense operators on a boolean algebra
Guram Bezhanishvili, Andre Kornell
We study the poset NO(B) of necessity operators on a boolean algebra B. We show that NO(B) is a meet-semilattice that need not be distributive. However, when B is complete, NO(B) i…
Completely hereditarily atomic OMLs
John Harding, Andre Kornell
An irreducible complete atomic OML of infinite height cannot both be algebraic and have the covering property. However, Kalmbach's construction provides an example of such an OML t…
Axioms for the category of sets and relations
Andre Kornell
We provide axioms for the dagger category of sets and relations that recall recent axioms for the dagger category of Hilbert spaces and bounded operators.
Axioms for the category of Hilbert spaces and linear contractions
Chris Heunen, Andre Kornell, Nesta van der Schaaf
The category of Hilbert spaces and linear contractions is characterised by elementary categorical properties that do not refer to probabilities, complex numbers, norm, continuity,…
A natural deduction system for orthomodular logic
Andre Kornell
Orthomodular logic is a weakening of quantum logic in the sense of Birkhoff and von Neumann. Orthomodular logic is shown to be a nonlinear noncommutative logic. Sequents are given…
Quantum CPOs
Andre Kornell, Bert Lindenhovius, Michael Mislove
We introduce the monoidal closed category qCPO of quantum cpos, whose objects are "quantized" analogs of omega-complete partial orders (cpos). The category qCPO is enriched over th…
Axioms for the category of Hilbert spaces
Chris Heunen, Andre Kornell
We provide axioms that guarantee a category is equivalent to that of continuous linear functions between Hilbert spaces. The axioms are purely categorical and do not presuppose any…
Semantics for Variational Quantum Programming
Xiaodong Jia, Andre Kornell, Bert Lindenhovius +2
We consider a programming language that can manipulate both classical and quantum information. Our language is type-safe and designed for variational quantum programming, which is…
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…
A complete system of deduction for Sigma formulas
Andre Kornell
The Sigma formulas of the language of arithmetic express semidecidable relations on the natural numbers. More generally, whenever a totality of objects is regarded as incomplete, t…
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…
The transfinite mean
Andre Kornell
We define a generalization of the arithmetic mean to bounded transfinite sequences of real numbers. We show that every probability space admits a transfinite sequences of points su…
On sequents of formulas
Andre Kornell
We investigate the position that foundational theories should be modelled on ordinary computability. In this context, we investigate the metamathematics of formulas. We conside…