Error bounds for Lie Group representations in quantum mechanics

Autor:	van Luijk, Lauritz, Galke, Niklas, Hahn, Alexander, Burgarth, Daniel
Rok vydání:	2022
Předmět:	Quantum Physics Mathematical Physics
Zdroj:	Journal of Physics A: Mathematical and Theoretical 57, 105301 (2024)
Druh dokumentu:	Working Paper
DOI:	10.1088/1751-8121/ad288b
Popis:	We provide state-dependent error bounds for strongly continuous unitary representations of connected Lie groups. That is, we bound the difference of two unitaries applied to a state in terms of the energy with respect to a reference Hamiltonian associated to the representation and a left-invariant metric distance on the group. Our method works for any connected Lie group and the metric is independent of the chosen representation. The approach also applies to projective representations and allows us to provide bounds on the energy constrained diamond norm distance of any suitably continuous channel representation of the group. Comment: 31 pages, 2 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2211.08582 Zobrazit plný text záznamu View this record from Arxiv