UNCERTAINTY RELATIONS BEYOND HEISENBERG: A Geometric Formulation of the Uncertainty Principle.

BOSYK, GUSTAVO MARTÍN

Grenoble

Seminario; Réunion Cics, Gipsa-Lab; 2014

GIPSA-Lab

The uncertainty principle lies at the heart of quantum mechanics, and it is a characteristic of the quantum world without classical analogue. It establishes that the probability distributions associated with the outcomes of two incompatible observables cannot be simultaneously sharp. Originally it has been formulated in terms of variances of quantum observables leading to the well-known Heisenberg-Robertson Uncertainty Relation. However, this formulation presents some drawbacks and does not capture the essence of the principle in typical situations. The aim of this talk is to present a geometric viewpoint that overcomes the drawbacks of the original formulation and leads to fidelity-based uncertainty relations, which are valid for pure states and for mixed states.