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QI: Fachverband Quanteninformation

QI 17: Quantum Information: Concept and Methods I

QI 17.3: Talk

Wednesday, March 20, 2024, 10:00–10:15, HFT-TA 441

Achievable state transformations under rotational invariance — •Fynn Otto and Konrad Szymański — Universität Siegen, Germany

Rotational invariance is a fundamental characteristic of physical interactions, naturally leading to rotationally covariant dynamics. In communication between distant parties, the lack of a common reference frame imposes similar constraints on the effective transformations: they must be independent of the unknown reference, and thus are rotationally covariant as well. This feature is captured by the formalism of SU(2)-covariant operations: those that commute with the actions of all group elements. We present an analytical characterization of covariant transformations and introduce semidefinite programs to examine which states are reachable from a given input using SU(2) -covariant channels. Our results improve our understanding of the transformations of directional information carriers and showcase the mechanisms of quantum operations lacking a reference frame.

Keywords: semidefinite progamming; rotational symmetry; polynomial theory; resource theory; covariant channels