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

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

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Geometric us polo assn mens sweaters 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 icon track bar f250 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.