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Preparational Uncertainty Relations for N Continuous Variables

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Preparational Uncertainty Relations for N Continuous Variables. / Kechrimparis, Spyridon; Weigert, Stefan.

In: Mathematics, 19.07.2016, p. 1-17.

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Harvard

Kechrimparis, S & Weigert, S 2016, 'Preparational Uncertainty Relations for N Continuous Variables', Mathematics, pp. 1-17. https://doi.org/10.3390/math4030049

APA

Kechrimparis, S., & Weigert, S. (2016). Preparational Uncertainty Relations for N Continuous Variables. Mathematics, 1-17. https://doi.org/10.3390/math4030049

Vancouver

Kechrimparis S, Weigert S. Preparational Uncertainty Relations for N Continuous Variables. Mathematics. 2016 Jul 19;1-17. https://doi.org/10.3390/math4030049

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Kechrimparis, Spyridon ; Weigert, Stefan. / Preparational Uncertainty Relations for N Continuous Variables. In: Mathematics. 2016 ; pp. 1-17.

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@article{5704d027dfd449e0be04e0d3e5d0e623,
title = "Preparational Uncertainty Relations for N Continuous Variables",
abstract = "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 which allow one to distinguish entangled from separable states. We also investigate the geometry of the {"}uncertainty region{"} in the N(2N+1)-dimensional space of moments. It is shown to be a convex set for any number continuous variables, and the points on its boundary 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 pace of second moments.",
author = "Spyridon Kechrimparis and Stefan Weigert",
note = "{\circledC} 2016, The Author(s).",
year = "2016",
month = "7",
day = "19",
doi = "10.3390/math4030049",
language = "English",
pages = "1--17",
journal = "Mathematics",
issn = "2227-7390",
publisher = "MDPI AG",

}

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TY - JOUR

T1 - Preparational Uncertainty Relations for N Continuous Variables

AU - Kechrimparis, Spyridon

AU - Weigert, Stefan

N1 - © 2016, The Author(s).

PY - 2016/7/19

Y1 - 2016/7/19

N2 - 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 which allow one to distinguish entangled from separable states. We also investigate the geometry of the "uncertainty region" in the N(2N+1)-dimensional space of moments. It is shown to be a convex set for any number continuous variables, and the points on its boundary 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 pace of second moments.

AB - 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 which allow one to distinguish entangled from separable states. We also investigate the geometry of the "uncertainty region" in the N(2N+1)-dimensional space of moments. It is shown to be a convex set for any number continuous variables, and the points on its boundary 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 pace of second moments.

U2 - 10.3390/math4030049

DO - 10.3390/math4030049

M3 - Article

SP - 1

EP - 17

JO - Mathematics

T2 - Mathematics

JF - Mathematics

SN - 2227-7390

ER -