Resource theory of quantum coherence: results based on the majorization lattice

BOSYK, G M

Vaxjoo

Conferencia; Quantum Information and Probability: from Foundations to Engineering (QIP23); 2023

Linnaeus University

Two of the main problems in the resource theory of quantum coherence are thecharacterization of the conversions between coherent states (resources) using the incoherentoperations (free operations) and the quantification of these resources. In this presentation, weutilize the majorization lattice theory [1] to address these issues. We introduce the concept ofgeneralized coherence vector [2], which fully characterizes the notions of incoherent andmaximally coherence states. Furthermore, we establish a necessary condition for convertinggeneral quantum states using incoherent operations, based on a majorization relation betweenthe generalized coherence vectors associated to the initial and final states. Finally, we proposea family of coherence quantifiers from concave and symmetric functions applied to thegeneralized coherence vector.[1] G.M. Bosyk, G. Bellomo, F. Holik, H. Freytes, G. Sergioli, New. J. Phys. 21, 083028 (2019).[2] G.M. Bosyk, M. Losada, C. Massri, H. Freytes, G. Sergioli, Phys. Rev. A 103, 012403(2021).