Abstract
[EN] 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.