Hannover 2020 – scientific programme
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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 qutrit — Christopher Eltschka1, Marcus Huber2, Simon Morelli2, and •Jens Siewert3,4 — 1University 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.