1302.2074 (Ole Andersson et al.)

Geometric uncertainty relation for mixed quantum states    [PDF]

Ole Andersson, Hoshang Heydari

The phase space of a unitarily evolving quantum system in a mixed state consists of isospectral density operators. In this paper we equip the spaces of isospectral density operators with natural Riemannian and symplectic structures, and we derive a geometric uncertainty relation for observables acting on systems in mixed states. Moreover, we give a geometric proof of the Robertson-Schr\"{o}dinger uncertainty relation, and we compare the two uncertainty relations.

View original: http://arxiv.org/abs/1302.2074