Preparational Uncertainty Relations for N Continuous Variables
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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2016-07-01
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| Series: | Mathematics |
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| Online Access: | http://www.mdpi.com/2227-7390/4/3/49 |
| _version_ | 1819098039098277888 |
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| author | Spiros Kechrimparis Stefan Weigert |
| author_facet | Spiros Kechrimparis Stefan Weigert |
| author_sort | Spiros Kechrimparis |
| collection | DOAJ |
| description | 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 N ( 2 N + 1 ) -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. |
| first_indexed | 2024-12-22T00:24:38Z |
| format | Article |
| id | doaj.art-89f62d6b0c4b4f608911aeb01ac2a6cc |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-22T00:24:38Z |
| publishDate | 2016-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-89f62d6b0c4b4f608911aeb01ac2a6cc2022-12-21T18:45:05ZengMDPI AGMathematics2227-73902016-07-01434910.3390/math4030049math4030049Preparational Uncertainty Relations for N Continuous VariablesSpiros Kechrimparis0Stefan Weigert1Department of Mathematics, University of York, York YO10 5DD, UKDepartment of Mathematics, University of York, York YO10 5DD, UKA 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 N ( 2 N + 1 ) -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.http://www.mdpi.com/2227-7390/4/3/49quantum uncertaintyconvexityentanglement detection |
| spellingShingle | Spiros Kechrimparis Stefan Weigert Preparational Uncertainty Relations for N Continuous Variables Mathematics quantum uncertainty convexity entanglement detection |
| title | Preparational Uncertainty Relations for N Continuous Variables |
| title_full | Preparational Uncertainty Relations for N Continuous Variables |
| title_fullStr | Preparational Uncertainty Relations for N Continuous Variables |
| title_full_unstemmed | Preparational Uncertainty Relations for N Continuous Variables |
| title_short | Preparational Uncertainty Relations for N Continuous Variables |
| title_sort | preparational uncertainty relations for n continuous variables |
| topic | quantum uncertainty convexity entanglement detection |
| url | http://www.mdpi.com/2227-7390/4/3/49 |
| work_keys_str_mv | AT spiroskechrimparis preparationaluncertaintyrelationsforncontinuousvariables AT stefanweigert preparationaluncertaintyrelationsforncontinuousvariables |