2013/08/31 by G. M. Bosyk, T. M. Osán, P. W. Lamberti +1
Physics and Astronomy · #quant-ph
paper · pdf · doi:10.1103/physreva.89.034101
8 pages, 1 figure
arxiv created 2013/10/11 · arxiv updated 2015/06/16
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 ones, 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 re-obtain 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 novel uncertainty relations when using other known fidelity-based metrics.