AG Mathematische Physik, Lauritz van Luijk (Perimeter Institute): Entanglement in von Neumann Algebraic Quantum Information Theory

Lauritz van Luijk (Perimeter Institute)

Entanglement in von Neumann Algebraic Quantum Information Theory

Abstract:
I will present results from a recent series of works with Alexander
Stottmeister, Reinhard F. Werner, and Henrik Wilming in which we study
bipartitions of quantum systems with an infinite number of degrees of freedom
from an information-theoretic perspective. Our goal is to understand the
interplay between information-theoretic properties of the physical systems and
algebraic properties of the von Neumann algebras describing them. I will
present two developments:
(1) A bijective correspondence between the classification of factors into types
and subtypes and a set of operational entanglement properties. For instance,
Connes’ classification of type III factors corresponds to the smallest
achievable error when trying to ’embezzle’ entanglement from the system.
(2) A result from my PhD thesis showing that the von Neumann algebraic
description of subsystems can be derived from a set of model-independent
operational axioms.