Noncommutative Analysis: Operator Systems and Nonlocality

Welcome to our team's website!

Operator Systems, i.e., unital selfadjoint linear spaces of Hilbert space operators, have been prominent in the theory of Hilbertian operators since their introduction by Arveson in the 1960’s and the cornerstone characterisation given subsequently by Choi and Effros. They provide a context for encoding and analysing data, offering effective models in cases where an algebraic structure may be inherently absent. 

The study of Operator Systems is witnessing a vast development in recent years. This is due on the one hand in the realisation that several key problems in Operator Algebra Theory could be advantageously formulated in terms of operator systems, and on the other in the discovery of a very large number of connections between abstract operator system theory and questions in the mathematical theory of Quantum Information, in particular through the apparatus of non-commutative graphs, non-local games and Zero-error Quantum Information Theory. One of the key underlying ideas that feeds into these areas is the identification of operator systems up to stabilizations and has been only recently brought to focus. In the current project, we elaborate on two aspects of operator systems that have recently become prominent in theory and applications. 

Our research project divides into two parts: Δ-equivalence for Operator Systems, and Quantum Information Theory. Namely, in the first part of the project we delve in the representation theory of Operator Systems, outlining several questions of importance at the level of their categorical perception. The second part of the project seeks to develop a formal mathematical framework that allows the study of no-signalling correlations from quantum physics in the presence of a generalised non-locality, where the participating and interacting parties of a quantum system are modelled by a hypergraph.

Members: 

• Michael Anoussis, University of the Aegean

• Alexandros Chatzinikolaou, National and Kapodistrian University of Athens

• George K. Eleftherakis, University of Patras

• Evgenios Kakariadis, Newcastle University

• Aristides Katavolos,  National and Kapodistrian University of Athens

• Nikolaos Koutsonikos-Kouloumpis, University of Patras

• Ioannis Apollon Paraskevas, National and Kapodistrian University of Athens

• Ivan G. Todorov, University of Delaware

Principal investigator: Michael Anoussis                                                                                             Host Institution: University of the Aegean

This project is carried out within the framework of the National Recovery and Resilience Plan Greece 2.0, funded by the European Union – NextGenerationEU (Implementation body: HFRI). Budget: 166.000€