Presented by:
René Schwonnek
Date:
Monday 23rd July 2018 - 16:00 to 16:45
Venue:
INI Seminar Room 1
Abstract:
We
consider the uncertainty between two pairs of local projective measurements
performed on a multipartite system. We show that the optimal bound in any
linear uncertainty relation, formulated in terms of the Shannon entropy, is
additive. This directly implies, against naive intuition, that the minimal
entropic uncertainty can always be realized by fully separable states. Hence,
in contradiction to proposals by other authors, no entanglement witness can be
constructed solely by comparing the attainable uncertainties of entangled and
separable states. However, our result gives rise to a huge simplification for
computing global uncertainty bounds as they now can be deduced from local ones.
Furthermore, we provide the natural generalization of the Maassen and Uffink
inequality for linear uncertainty relations with arbitrary positive
coefficients.
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