Geometric formulation of uncertainty principle

BOSYK, GUSTAVO MARTÍN; PORTESI, MARIELA; OSÁN, TRISTÁN MARTÍN; LAMBERTI. PEDRO WALTER

Paraty

Workshop; IV Quantum Information, School and Workshop; 2013

A geometric approach to formulate the Uncertainty Principle for two quantum observables on an N-dimensional Hilbert space is proposed [1]. We consider the delity between a density operator for the quantum system and some observable projector, and interpret it as the probability of obtaining the corresponding outcome. We derive a family of uncertainty relations by using the triangle inequality for fidelity-based metrics. In the case of Wootters metric, we re-obtain the Landau-Pollak inequality relation for pure states and show in a natural way its validity for mixed states as well. In addition, we derive novel uncertainty relations when using other available metrics.