Quantum correlations and the Bloch representation of quantum states

• Applicant: Dr. Christopher Eltschka
• Subject Area: Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas
• Term: from 2016 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 311953832

Quantum correlations are at the heart of the physics of composite systems. Entanglement arguably is the most striking -and at the same time most wellknown - type of quantum correlations. A thorough understanding of entanglement is not only one of the key issues in the foundations of quantum mechanics, but is also of practical relevance in diverse fields of physics.In this project, we aim at new mathematical results for the correlation properties of quantum states by merging two hitherto distinct branches of entanglement theory: entanglement quantification via pure-state measures vs. methods based on the partial transpose.This will be done by boosting the formal development of the Bloch representation and thus gaining new insight into quantum correlations from a geometry-inspired point of view. A specific goal of our work is to make the Bloch representation accessible by developing hands-on rules for the algebraic and geometric properties of quantum states.As of now the objective of our project in combination with this approach is unique. In order to pave the way to obtain results in this largely unexplored field we envisage three work packages:* Monogamy equalities for qubits and multipartite systems of higher dimension,* Exact investigation of states with positive partial transpose in terms of entanglement measures,* Highlighting the relation between local SL-invariant vs. other entanglement measures; in-depth study of the so-called normal form of multipartite quantum states and its relevance for non-SL-invariant quantities.

• DFG Programme: Research Grants
• International Connection: Spain
• Cooperation Partner: Professor Dr. Jens Siewert