### International Quantum Structures Association

The Birkhoff-von Neumann Prize prize is awarded once every two years during the award ceremony held at the bi-annual conference of the International Quantum Structures Association (IQSA). The candidates for the prize are selected by the IQSA prize committee for their outstanding scientific achievements in the field of quantum structures and the impact their work has on the research in quantum logic and quantum foundations.

## Winner for 2024

The "Birkhoff-von Neumann Prize 2024" was awarded to Dr. Andre Kornell. The Award Ceremony of the "Birkhoff-von Neumann Prize 2024" took place on Wednesday 24 July, during the 16th Biennial Meeting of the International Quantum Structures Association in Brussels, Belgium.

## Andre Kornell

Andre Kornell earned his doctorate in mathematics from Berkeley in 2015, and then worked at UC Davis as a visiting professor and lecturer until 2019, and then in sponsored postdoctoral positions at Tulane under Michael Mislove and Dalhousie under Peter Selinger. His work spans a number of directions in the quantum structures universe from the applied to foundational.

In his thesis, Operator algebras in Solovay’s model, Kornell develops the theory of analogs of von Neumann algebras in a model of set theory where a continuum-weak topology has meaning. In work related to foundations of quantum programming languages, he has co-authored papers on quantum complete partial orders and semantics for variational quantum programming. In the mainstream of quantum information, he has a recent preprints characterizing homomorphisms among completely positive maps and is co-author on a paper describing improvements to product formulas circuits for Hamiltonian simulation. Joint work with Chris Heunen appearing in the Proceedings of the National Academy of Sciences axiomatizes the category of Hilbert spaces and bounded linear maps, with subsequent work characterizing the category of Hilbert spaces and linear contractions. In what has likely been his primary interest, Kornell has an ambitious series of half a dozen papers developing a quantum version of set theory with accompanying logic in which structures externally viewed as quantum are internally classical. Andre has additional papers related to orthomodular lattices and orthomodular spaces, as well as in more traditional logic.

Andre has an original body of work from the applied to foundational, encompassing a wide array of mathematics to address issues in quantum structures. He is a most deserving recipient of the Birkhoff-von Neumann Prize.”

Winner for 2022

The "Birkhoff-von Neumann Prize 2022" was awarded to Dr. Jamie Vicary. The Award Ceremony of the "Birkhoff-von Neumann Prize 2022" took place on Wednesday 29 June, during the 15th Biennial Meeting of the International Quantum Structures Association in Tropea, Italy.

__Jamie Vicary__

received his PhD under Chris Isham at Imperial. After his PhD he held positions at Oxford, Birmingham, and is currently a Royal Society Research Fellow and Associate Professor of Programming at Cambridge and a Senior Research Fellow in the department of Computer Science at Oxford where he is a member of the Quantum Group. Jamie's research has centered around the use of category theory in quantum computing and information. To my view, Jamie's research is typified by finding what in hindsight is a natural question, providing an elegant solution, then writing it ever so clearly to make everything seem natural. In an area that can at times be opaque, Jamie's work is a source of illumination. Among Jamie's 40 some publications, there are many highlights. To name just a few: 1) Physical assumptions on a category that imply the existence of the complex numbers. 2) Connections between Frobenius algebras, bases and finite-dimensional C*-algebras in the category of finite-dimensional Hilbert spaces. 3) Quantum Latin squares and error bases. 4) A book with Chris Heunen on categorical quantum mechanics. 5) Work on 2-categorical views of quantum processes. In sum, Jamie is a primary figure in the second (or is it third or fourth) wave of quantum structures, and a most deserving recipient of the Birkhoff-von Neumann Prize.

Winner for 2018

__Francesco Buscemi__

is Associate Professor at the Department of Mathematical Informatics of Nagoya University, Japan. His results solved some long-standing open problems in the foundations of quantum physics, using ideas from mathematical statistics and information theory. He established, in a series of single-authored papers, the theory of quantum statistical morphisms and quantum statistical comparison, generalizing to the noncommutative setting some fundamental results in mathematical statistics dating back to works of David Blackwell and Lucien Le Cam. In particular, Prof. Buscemi successfully applied his theory to construct the framework of "semiquantum nonlocal games," which extend Bell tests and are now widely used in theory and experiments to certify, in a measurement device-independent way, the presence of non-classical correlations in space and time.

Winners for 2016

__Markus Muller__

holds a Canada Research Chair in the "Foundations of Physics" at the University of Western Ontario, where he holds a joint appointment in the departments of Applied Mathematics and Philosophy. He received his doctorate from TU Berlin in 2007 and held post-doctoral positions at the Max Plank Institute, the University of Potsdam, and the Perimeter Institute, as well as a position as junior research group leader at the University of Heidelberg. Dr. Muller has established himself, in a remarkably short time, as one of the leading figures working at the intersection of quantum information theory and the foundations of quantum theory. His work includes one of the first information-theoretic reconstructions of finite-dimensional quantum theory, the Muller-Ududec Theorem on the self-duality of finite-dimensional state spaces, the undecidability of quantum measurement results, an operational account of the origin of spacetime symmetries, results on non-equilibrium quantum thermodynamics, and a characterization of quantum theory in terms of (the absence of) higher-order interference.

__Paolo Perinotti__

is assistant professor of "Theoretical Physics of Information" at the University of Pavia (Italy). In his rich research-activity he has obtained some original and outstanding results that concern in particular: 1) the formulation of quantum theory from information-theoretical operational axioms; 2) the development and application of "quantum comb theory" for the representation of general quantum processes, with or without definite causal structures; 3) the derivation of the relativistic quantum equations of Weyl, Dirac and Maxwell from the structure of quantum cellular automata, and the study of the emergence of their dynamical and symmetry properties; 5) the formulation of fermionic quantum theory as an operational probabilistic theory and its application to the study of fermionic entanglement.

Winners for 2014

__Weihua Liu__

Was a PhD student at the Department of Mathematics of the University of California, Berkeley (US). His contributions include some very interesting and original results that concern the existence of the supremum of two elements in quantum effect algebras. He has also proved two nice representation theorems for the supremum and infimum of bounded quantum observables.

__Anna Jencova__

is a researcher at the Mathematical Institute of the Slovak Academy of Sciences, Bratislava (Slovakia). In her rich scientific activity she has obtained some highly significant and original results that concern non-commutative extensions of information geometry. More recently she has investigated some important problems of statistical decision theory for general quantum objects.

## Winners for 2012

__Chris Heunen__

(University of Oxford) - His research work from a few years ago, mainly in the past couple of years, is quantitatively impressive, very close to the core themes of IQSA, and of high quality. It includes a variety of problems and results deserving great appreciation: in particular, the study of the embedding of axiomatically defined Hilbert categories into Hilbert spaces, the study of how algebraic quantum mechanics can be related to topos theory so as to construct new foundations for quantum logic, the analysis of quantum logic from the perspective of categorial logic.

__Sonja Smets__

(University of Amsterdam - Institut for Logic, Language and Computation) - For her studies on quantum structures and related epistemic semantics which gave rise to a number of remarkable original results. In particular, new light emerged on - a dynamical interpretation of quantum-logical connectives, - a link between quantum logic and quantum computation, - a logical analysis of classical and quantum correlations - an epistemic-logic view of quantum entanglement, - a reduction of the complexity of the Soler-Mayet axiomatization.