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Hannover 2020 – scientific programme

The DPG Spring Meeting in Hannover had to be cancelled! Read more ...

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Q: Fachverband Quantenoptik und Photonik

Q 8: Quantum Information (Concepts and Methods) II

Q 8.7: Talk

Monday, March 9, 2020, 15:30–15:45, e001

The shape of higher-dimensional state space – Bloch sphere analog for a qutritChristopher Eltschka1, Marcus Huber2, Simon Morelli2, and •Jens Siewert3,41University of Regensburg, 93053 Regensburg, Germany — 2IQOQI Vienna, Austrian Academy of Sciences, 1090 Vienna, Austria — 3University of the Basque Country UPV/EHU, 48080 Bilbao, Spain — 4IKERBASQUE Basque Foundation for Science, 48013 Bilbao, Spain

The Bloch sphere 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. This is difficult because, in order to serve as a model for the state space, it should display a number of desirable properties, such as different surface parts corresponding to pure or mixed states, convexity, insphere and outsphere 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.

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