Modular Time and Quantum Information

This video is part of the PROTEUS project that has received funding from the European Research Council (ERC) under the Horizon 2020 research and innovation programme (Grant agreement No. 758145)

Abstract

The fundamental new structure at the basis of Quantum Mechanics is Noncommutativity. Von Neumann algebras are non commutative measure spaces. In 1967 Tomita uncovered a deep, surprising structure: every state of a von Neumann algebra gives raise to an evolution, trivial in the commutative case. So we have an intrinsic “modular time” that has a quantum thermodynamical interpretation. After a general introduction, I will present recent results on Quantum Information for systems with infinitely many degrees of freedom that are based on the Tomita-Takesaki modular theory.