Absolutely dilatable module maps

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• Lyudmila Turowska (Chalmers University of Technology)
• Thursday 05 December 2024, 16:00-17:00
• Seminar Room 1, Newton Institute.

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QIAW02 - New trends at the intersection of quantum information theory, quantum groups and operator algebras

I will discuss the notion of absolute dilation for maps on von Neumann algebras, focusing primarily on maps on B(H) with an additional modularity condition. The notion was recently defined and studied by C. Duquet and C. Le Merdy. They characterized dilatable Schur multipliers. We extend the results by replacing the requirement of being Schur by being modular over arbitrary von Neumann algebra, instead of maximal abelian selfadjoint algebra.    Such maps   are characterized by the existence of a tracial von Neumann algebra (N, τ), called an ancilla, and a certain unitary operator. Different types of ancillas (abelian, finite-dimensional, etc.) lead to the definition of local, quantum, approximate quantum, and quantum commuting dilatable maps, and I will discuss the relationships between these types. The motivation to study different types of dilations comes from Quantum Information Theory. The talk is based on a project with A. Chatzinikolaou and I. G. Todorov.

This talk is part of the Isaac Newton Institute Seminar Series series.

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