LAMBERTI Pedro Walter
Geometric formulation of the uncertainty principle
G.M. BOSYK; TRISTAN OSAN; PEDRO W. LAMBERTI; MARIELA PORTESI
PHYSICAL REVIEW A - ATOMIC, MOLECULAR AND OPTICAL PHYSICS
AMER PHYSICAL SOC
Lugar: New York; Año: 2014 vol. 89 p. 341011 - 341015
A geometric approach to formulate the uncertainty principle between quantum observables acting on an N-dimensional Hilbert space is proposed. We consider the fidelity between a density operator associated with a quantum system and a projector associated with an observable, and interpret it as the probability of obtaining the outcome corresponding to that projector. We make use of fidelity-based metrics such as angle, Bures, and root infidelity to propose a measure of uncertainty. The triangle inequality allows us to derive a family of uncertainty relations. In the case of the angle metric, we recover the Landau-Pollak inequality for pure states and show, in a natural way, how to extend it to the case of mixed states in arbitrary dimension. In addition, we derive and compare alternative uncertainty relations when using other known fidelity-based metrics.