IX International Workshop on Information Geometry, Quantum Mechanics and Applications 2025
24 - 28 February 2025
Universidad Carlos III
About IWIGQMA2025
The International Workshop on Information Geometry, Quantum Mechanics and Applications
is part of a series of meetings on Quantum Mechanics and its applications that are held annually either at Policeta (Italy) or Madrid. It is an international meeting devoted to the study of the mathematical foundations of Quantum Mechanics and their applications, many of them instrumental in the emergent problems related to Quantum Information Technologies. The objective of this workshop is to present a few relevant problems in the foundations of Quantum Mechanics to a small number of young researchers (Post and Pre doctoral) and to work in a collaborative environment.
Main Topics
- Classical and quantum information geometry/theory
- Categorical approaches to quantum (field) theories, probability, and information theory.
- Quantum Dynamics of Closed and Open Systems
- The Quantum-to-Classical Transition.
Mini Course 1: Tobias Fritz (University of Innsbruck)
Introduction to Markov Categories
Video Recording
Mini Course 2: Urs Schreiber (New York University in Abu Dhabi)
Quantum Language via Linear Homotopy Types
It is well-appreciated that (intuitionistic but otherwise) classical (functional, programming) language is essentially the internal logic to cartesian closed categories (of data types), in particular to (higher) toposes — and that epistemology and other modality expressing physical observations and effects are reflected by (idempotent) co/monads on these categories. In the course we explore how this classical situation naturally extends to subsume quantum logic of quantum systems controlled and measured by classical observers: Here doubly closed monoidal categories (of entangled quantum data types parameterized by classical data), such as higher tangent toposes, reflect in their linear slices the substructural (no-deleting/no-cloning) quantum coherence, while their base change co/monads between linear slices turn out to know everything about decoherent quantum measurement (wave function collapse), including the ancient Born rule as well as contemporary spider-fusion in ZX-calculus string diagrams. Further pointers and notes may be found at ncatlab.org/schreiber/show/Quantum+Language+via+Linear+Homotopy+Types.