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 Geometric uncertainty relation for mixed quantum states


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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.



Author: Ole Andersson; Hoshang Heydari

Source: https://archive.org/







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