A geometric formulation of uncertainty principle

GUSTAVO M. BOSYK; PEDRO W. LAMBERTI; TRISTÁN M. OSÁN; MARIELA PORTESI

Rio de Janeiro

Workshop; IV Quantum Information School and Workshop - Paraty 2013; 2013

UNICAMP-UFRJ

A geometric approach to formulate the uncertainty principle between quantum observables on an N-dimensional Hilbert space is proposed. We consider the fidelity between a density operator for the 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 reobtain the Landau-Pollak uncertainty relation for pure states and show in a natural way its validity for mixed states. In addition, we derive novel uncertainty relations when using other known metrics.