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QI: Fachverband Quanteninformation

QI 35: Quantum Information: Concepts and Methods II

QI 35.5: Vortrag

Donnerstag, 13. März 2025, 15:30–15:45, HS IV

Exploring Imaginary Coordinates: Disparity in the Shape of Quantum State Space in Even and Odd Dimensions — Simon Morelli¹, Santiago Llorens², and •Jens Siewert^{3, 4} — ¹Atominstitut, Technische Universität Wien, 1020 Vienna, Austria — ²Física Teórica: Informació i Fenómens Quántics, Universitat Autónoma de Barcelona, 08193 Bellaterra, Spain — ³University of the Basque Country UPV/EHU and EHU Quantum Center, 48080 Bilbao, Spain — ⁴Ikerbasque, Basque Foundation for Science, 48013 Bilbao, Spain

The state of a finite-dimensional quantum system is described by a density matrix that can be decomposed into a real diagonal, a real off-diagonal and and an imaginary off-diagonal part. The latter plays a peculiar role. While it is intuitively clear that some of the imaginary coordinates cannot have the same extension as their real counterparts the precise relation is not obvious. We give a complete characterization of the constraints in terms of tight inequalities for real and imaginary Bloch-type coordinates. Our description entails a three-dimensional Bloch ball-type model for the state space. We uncover a surprising qualitative difference for the state-space boundaries in even and odd dimensions.

Keywords: Geometry of quantum-mechanical state space; Bloch representation