paper

The shape of higher-dimensional state space: Bloch-ball analog for a qutrit

arXiv:2012.00587 · doi:10.22331/q-2021-06-29-485

Abstract

Geometric intuition is a crucial tool to obtain deeper insight into many concepts of physics. A paradigmatic example of its power is the Bloch ball, the geometrical representation for the state space of the simplest possible quantum system, a two-level system (or qubit). However, already for a three-level system (qutrit) the state space has eight dimensions, so that its complexity exceeds the grasp of our three-dimensional space of experience. This is unfortunate, given that the geometric object describing the state space of a qutrit has a much richer structure and is in many ways more representative for a general quantum system than a qubit. In this work we demonstrate that, based on the Bloch representation of quantum states, it is possible to construct a three dimensional model for the qutrit state space that captures most of the essential geometric features of the latter. Besides being of indisputable theoretical value, this opens the door to a new type of representation, thus extending our geometric intuition beyond the simplest quantum systems.

10 pages, 5 figures; discussion of results improved, one new figure

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