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SU(2) uncertainty limits
KTH, School of Engineering Sciences (SCI), Applied Physics, Quantum Electronics and Quantum Optics, QEO.
KTH, School of Engineering Sciences (SCI), Applied Physics, Quantum Electronics and Quantum Optics, QEO.ORCID iD: 0000-0002-2082-9583
2016 (English)In: PHYSICAL REVIEW A, ISSN 2469-9926, Vol. 93, no 5, 052101Article in journal (Refereed) Published
Resource type
Text
Abstract [en]

Although progress has been made recently in defining nontrivial uncertainty limits for the SU(2) group, a description of the intermediate states bound by these limits remains lacking. In this paper we enumerate possible uncertainty relations for the SU(2) group that involve all three observables and that are, moreover, invariant under SU(2) transformations. We demonstrate that these relations however, even taken as a group, do not provide sharp, saturable bounds. To find sharp bounds, we systematically calculate the variance of the SU(2) operators for all pure states belonging to the N = 2 and N = 3 polarization excitation manifold (corresponding to spin 1 and spin 3/2). Lastly, and perhaps counter to expectation, we note that even pure states can reach the maximum uncertainty limit.

Place, publisher, year, edition, pages
American Psychological Association (APA), 2016. Vol. 93, no 5, 052101
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:kth:diva-188065DOI: 10.1103/PhysRevA.93.052101ISI: 000375523600001Scopus ID: 2-s2.0-84964912088OAI: oai:DiVA.org:kth-188065DiVA: diva2:943021
Note

QC 20160627

Available from: 2016-06-27 Created: 2016-06-03 Last updated: 2017-05-03Bibliographically approved
In thesis
1. Majorana Representation in Quantum Optics: SU(2) Interferometry and Uncertainty Relations
Open this publication in new window or tab >>Majorana Representation in Quantum Optics: SU(2) Interferometry and Uncertainty Relations
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The algebra of SU(2) is ubiquitous in physics, applicable both to the atomic spin states and the polarisation states of light. The method developed by Majorana and Schwinger to represent pure, symmetric spin-states of arbitrary value as a product of spin-1/2 states is a powerful tool that allows for a great conceptual and practical simplification. Foremost, it allows the representation of a qudit on the same geometry as a qubit, i.e., the Bloch sphere.

An experimental implementation of the Majorana representation in the realm of quantum optics is presented. The technique allows the projection of arbitrary quantum states from a coherent state input. It is also shown that the method can be used to synthesise arbitrary interference patterns with unit visibility, and without resorting to quantum resources. In this context, it is argued that neither the shape nor the visibility of the interference pattern is a good measure of quantumness. It is only the measurement scheme that allows for the perceived quantum behaviour.

The Majorana representation also proves useful in delineating uncertainty limits of states with a particular spin value. Issues with traditional uncertainty relations involving the SU(2) operators, such as trivial bounds for certain states and non-invariance, are thereby resolved with the presented pictorial solution.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2017. 66 p.
Series
TRITA-FYS, ISSN 0280-316X ; 2017:25
Keyword
Majorana representation, Quantum optics, interferometry, SU(2) group, angular momentum, arbitrary optical gates
National Category
Atom and Molecular Physics and Optics
Research subject
Physics
Identifiers
urn:nbn:se:kth:diva-206222 (URN)978-91-7729-367-5 (ISBN)
Public defence
2017-05-12, FA31, AlbaNova University Center, Roslagstullsbacken 21, Stockholm, 13:00 (English)
Opponent
Supervisors
Note

QC 20170428

Available from: 2017-04-28 Created: 2017-04-28 Last updated: 2017-04-28Bibliographically approved

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