  We express modular and weak values of observables of three- and higher-level
quantum systems in their polar form. The Majorana representation of N-level
systems in terms of symmetric states of N-1 qubits provides us with a
description on the Bloch sphere. With this geometric approach, we find that
modular and weak values of observables of N-level quantum systems can be
factored in N-1 contributions. Their modulus is determined by the product of
N-1 ratios involving projection probabilities between qubits, while their
argument is deduced from a sum of N-1 solid angles on the Bloch sphere. These
theoretical results allow us to study the geometric origin of the quantum phase
discontinuity around singularities of weak values in three-level systems. We
also analyze the three-box paradox [1] from the point of view of a bipartite
quantum system. In the Majorana representation of this paradox, an observer
comes to opposite conclusions about the entanglement state of the particles
that were successfully pre- and postselected.
