标题：Probability density functions of quantum mechanical observable uncertainties

作者：费少明 教授

简介：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 stateindependent

uncertainty relations. Our results may be generalized to multiple observable cases in

higher dimensional spaces.