Geometric approach to modular and weak values of discrete quantum systems

Mirko Cormann, Yves Caudano

Published 2016-12-21Version 1

We express modular and weak values of three- and high-level quantum systems in their polar form. Within the Majorana representation and a purely geometric approach, we point out that this complex values of N-level quantum systems possess a modulus determined by the product of N-1 square roots of probability ratios and an argument deduced from a sum of N-1 spherical polygons on the Bloch sphere. This theoretical results demonstrate that the discontinuous effects around singularities of weak values have a purely geometric origin with no classical counterpart. Furthermore, the geometric approach is used to extend the three-box paradox [1] to a larger class of quantum phenomena: quantum entanglement. Therefore, we present a two spin-1/2 measurement experiment, for which Alice and Bob come to counter-intuitive conclusions about the particles' state between pre- and postselection.