Preparational Uncertainty Relations for N Continuous Variables
Department of Mathematics, University of York, York YO10 5DD, UK
Author to whom correspondence should be addressed.
Academic Editors: Takayuki Miyadera and Teiko Heinosaari
Received: 31 March 2016 / Revised: 28 June 2016 / Accepted: 9 July 2016 / Published: 19 July 2016
A smooth function of the second moments of N
continuous variables gives rise to an uncertainty relation if it is bounded from below. We present a method to systematically derive such bounds by generalizing an approach applied previously to a single continuous variable. New uncertainty relations are obtained for multi-partite systems that allow one to distinguish entangled from separable states. We also investigate the geometry of the “uncertainty region” in the
-dimensional space of moments. It is shown to be a convex set, and the points on its boundary are found to be in one-to-one correspondence with pure Gaussian states of minimal uncertainty. For a single degree of freedom, the boundary can be visualized as one sheet of a “Lorentz-invariant” hyperboloid in the three-dimensional space of second moments.
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MDPI and ACS Style
Kechrimparis, S.; Weigert, S. Preparational Uncertainty Relations for N Continuous Variables. Mathematics 2016, 4, 49.
Kechrimparis S, Weigert S. Preparational Uncertainty Relations for N Continuous Variables. Mathematics. 2016; 4(3):49.
Kechrimparis, Spiros; Weigert, Stefan. 2016. "Preparational Uncertainty Relations for N Continuous Variables." Mathematics 4, no. 3: 49.
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