Réunion d'hiver SMC 2026

Montréal, 11 - 14 décembre 2026

       
La théorie des catégories supérieurs à travers les mathématiques
Org: Kristine Bauer (University of Calgary) et Martina Rovelli (University of Ottawa)
JULIE BERGNER, University of Virginia

RICK BLUTE, University of Ottawa

ELEFTHERIOS CHATZITHEODORIDIS, Virginia Commonwealth University

ROBIN COCKETT, University of Calgary

GEOFF CRUTTWELL, Mount Allison University

PEDRO BRUNIALTI LIMA DE ANDRADE, University of Virginia



MARTIN FRANKLAND, University of Regina

ADINA GOLDBERG, University of Toronto

STEFANO LUNEIA, University of Ottawa

DORETTE PRONK, Dalhousie University

CARLO MARIA SCANDOLO, University of Calgary
A general type-theoretic approach to higher-order quantum resources  [PDF]

Quantum resources exist in a hierarchy of multiple levels. At order zero, quantum states are transformed by linear maps (channels, or gates) in order to perform computations or simulate other states. At order one, gates and channels are transformed by linear maps (superchannels) in order to simulate other gates. To develop a full hierarchy of quantum resources, beyond those first two orders, and to account for the fact that quantum protocols can interconvert resources of different orders, we need a theoretical framework that addresses all orders in a uniform manner. We introduce a framework based on a system of types, which label the different kinds of objects that are present at different orders. Subsequently, we equip the framework with a parallel product operation that modifies and generalizes the tensor product so as to be operationally meaningful for maps of distinct and arbitrary orders.

PRIYAA SRINAVASAN, Tallinn University of Technology

KIMBALL STRONG, Cornell University

DANIEL TEXEIRA, Dalhousie University

DAVID WHITE, Queen’s University

INNA ZAKHAREVICH, Cornell University

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