Regensburg 2022 – scientific programme
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QI: Fachverband Quanteninformation
QI 9: Quantum Correlations
QI 9.4: Talk
Thursday, September 8, 2022, 10:15–10:30, H8
The shape of higher-dimensional state space: Bloch ball analog for a qutrit — Christopher Eltschka1, Marcus Huber2,3, Simon Morelli2,3, and •Jens Siewert4,5 — 1Institut für Theoretische Physik, Universität Regensburg, Regensburg, Germany — 2IQOQI Vienna, Vienna, Austria — 3Atominstitut TU Wien, Vienna, Austria — 4University of the Basque Country UPV/EHU and EHU Quantum Center, Bilbao, Spain — 5Ikerbasque, Basque Foundation for Science, Bilbao, Spain
The Bloch ball as a geometric representation of the state space for qubits is an ubiquitous tool to gain deeper insight and intuitive understanding of quantum-mechanical phenomena. Unfortunately, even for the next more complex system, the qutrit, such a geometric representation (rather than cross sections or projections) is not known. In order to serve as a model for higher-dimensional state space, it should display a number of desirable properties, such as different surface parts corresponding to pure or mixed states, convexity, inner and outer sphere with the corresponding radii, pure states should form a connected set, etc. [1]. We show that, based on the Bloch representation of qutrit states, such a model can be constructed that captures many of the geometric features discussed in Ref. [1].
[1] I. Bengtsson, S. Weis, K. Zyczkowski, Geometry of the Set of Mixed Quantum States: An Apophatic Approach. In: P. Kielanowski et al (eds) Geometric Methods in Physics. Trends in Mathematics (Birkhäuser, Basel, 2013).