dc.identifier.uri |
http://dx.doi.org/10.15488/1604 |
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dc.identifier.uri |
http://www.repo.uni-hannover.de/handle/123456789/1629 |
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dc.contributor.author |
Dammeier, Lars
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|
dc.contributor.author |
Schwonnek, René
|
|
dc.contributor.author |
Werner, Reinhard F.
|
|
dc.date.accessioned |
2017-05-31T11:36:50Z |
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dc.date.available |
2017-05-31T11:36:50Z |
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dc.date.issued |
2015 |
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dc.identifier.citation |
Dammeier, L.; Schwonnek, R.; Werner, R.F.: Uncertainty relations for angular momentum. In: New Journal of Physics 17 (2015), Nr. 9, 93046. DOI: https://doi.org/10.1088/1367-2630/17/9/093046 |
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dc.description.abstract |
In this work we study various notions of uncertainty for angular momentum in the spin-s representation of SU(2). We characterize the 'uncertainty regions' given by all vectors, whose components are specified by the variances of the three angular momentum components. A basic feature of this set is a lower bound for the sum of the three variances. We give a method for obtaining optimal lower bounds for uncertainty regions for general operator triples, and evaluate these for small s. Further lower bounds are derived by generalizing the technique by which Robertson obtained his state-dependent lower bound. These are optimal for large s, since they are saturated by states taken from the Holstein-Primakoff approximation. We show that, for all s, all variances are consistent with the so-called vector model, i.e., they can also be realized by a classical probability measure on a sphere of radius Entropic uncertainty relations can be discussed similarly, but are minimized by different states than those minimizing the variances for small s. For large s the Maassen-Uffink bound becomes sharp and we explicitly describe the extremalizing states. Measurement uncertainty, as recently discussed by Busch, Lahti and Werner for position and momentum, is introduced and a generalized observable (POVM) which minimizes the worst case measurement uncertainty of all angular momentum components is explicitly determined, along with the minimal uncertainty. |
eng |
dc.description.sponsorship |
ERC/DQSIM |
|
dc.description.sponsorship |
DFG/RTG/1991 |
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dc.description.sponsorship |
BMBF/Q.com-Q |
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dc.description.sponsorship |
DFG |
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dc.language.iso |
eng |
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dc.publisher |
Bristol : Institute of Physics Publishing |
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dc.relation.ispartofseries |
New Journal of Physics 17 (2015), Nr. 9 |
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dc.rights |
CC BY 3.0 Unported |
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dc.rights.uri |
https://creativecommons.org/licenses/by/3.0/ |
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dc.subject |
Angular momentum |
eng |
dc.subject |
Momentum |
eng |
dc.subject |
Quantum theory |
eng |
dc.subject |
Classical probabilities |
eng |
dc.subject |
Measurement uncertainty |
eng |
dc.subject |
Optimal lower bound |
eng |
dc.subject |
Optimal measurements |
eng |
dc.subject |
Output vectors |
eng |
dc.subject |
State-dependent |
eng |
dc.subject |
Uncertainty regions |
eng |
dc.subject |
Uncertainty relation |
eng |
dc.subject |
Uncertainty analysis |
eng |
dc.subject |
angular momentum |
eng |
dc.subject |
quantum mechanics |
eng |
dc.subject |
uncertainty relations |
eng |
dc.subject.ddc |
530 | Physik
|
ger |
dc.title |
Uncertainty relations for angular momentum |
eng |
dc.type |
Article |
|
dc.type |
Text |
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dc.relation.issn |
1367-2630 |
|
dc.relation.doi |
https://doi.org/10.1088/1367-2630/17/9/093046 |
|
dc.bibliographicCitation.issue |
9 |
|
dc.bibliographicCitation.volume |
17 |
|
dc.bibliographicCitation.firstPage |
93046 |
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dc.description.version |
publishedVersion |
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tib.accessRights |
frei zug�nglich |
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