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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 11: Quantum Information

MP 11.2: Talk

Wednesday, September 1, 2021, 16:55–17:20, H7

Exploring the Limits of Open Quantum Dynamics II: Gibbs-Preserving Maps from the Perspective of Majorization — •Frederik vom Ende — TU Munich, 85748 Garching, Germany — Munich Centre for Quantum Science and Technology, 80799 Munich, Germany

Motivated by reachability questions in coherently controlled open quantum systems coupled to a thermal bath, as well as recent progress in the field of thermo-/vector-d-majorization (arXiv:1911.01061) we generalize classical majorization from unital quantum maps to maps with an arbitrary fixed point of full rank. Such maps preserve some Gibbs-state and thus play an important role in the resource theory of quantum thermodynamics, in particular for thermo-majorization.

Based on this we investigate D-majorization on matrices in terms of its topological and order properties, such as existence of unique maximal and minimal elements, etc. In the process we relate the notion of strict positivity to such maps as well as to Markovian processes in general. Moreover we characterize D-majorization in the qubit case via the trace norm and elaborate on why this is a challenging task when going beyond two dimensions.