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Applications of Functional Analysis to Quantum Information Theory

Grant number: 19/09205-0
Support type:Scholarships abroad - Research Internship - Post-doctor
Effective date (Start): October 01, 2019
Effective date (End): January 27, 2020
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal Investigator:Valentin Raphael Henri Ferenczi
Grantee:Willian Hans Goes Corrêa
Supervisor abroad: Carlos Palazuelos Cabezon
Home Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Research place: Universidad Complutense de Madrid (UCM), Spain  
Associated to the scholarship:18/03765-1 - Twisted Hilbert and complexity in Banach spaces, BP.PD

Abstract

Information theory deals with the storage and transmission of information. Quantum mechanics allowed the use of new resources to this area: in the classical model the unit of information is a bit, which assumes values 0 or 1, while in the quantum version the unit of information is a qubit, which assumes any value in the complex sphere. This is justified by the fact that in quantum mechanics the state of a system is a unitary vector in a Hilbert space. This project has as aim to explore connections between functional analysis and quantum information theory, with a focus of applying complex interpolation and twisted sums of operator spaces to this area.