Author:
Zhang Lin,Huang Jinping,Wang Jiamei,Fei Shao-Ming
Abstract
Abstract
We study the uncertainties of quantum mechanical observables, quantified by the standard deviation (square root of variance) in Haar-distributed random pure states. We derive analytically the probability density functions (PDFs) of the uncertainties of arbitrary qubit observables. Based on these PDFs, the uncertainty regions of the observables are characterized by the support of the PDFs. The state-independent uncertainty relations are then transformed into the optimization problems over uncertainty regions, which opens a new vista for studying state-independent uncertainty relations. Our results may be generalized to multiple observable cases in higher dimensional spaces.
Funder
Natural Science Foundation of Beijing Municipality
National Natural Science Foundation of China
Natural Science Foundation of Hubei Province
Subject
Physics and Astronomy (miscellaneous)