Research output: Contribution to journal › Article

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

Research output: Contribution to journal › Article

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

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

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

@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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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 -