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Configurations in Quantum Information
Stockholm University, Faculty of Science, Department of Physics. (Quantum Information and Quantum Optics)
2012 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Measurements play a central role in quantum information. This thesis looksat two types: contextual measurements and symmetric measurements. Contextualityoriginates from the Kochen-Specker theorem about hidden variablemodels and has recently undergone a subtle shift in its manifestation. Symmetricmeasurements are characterised by the regular polytopes they formin Bloch space (the vector space containing all density matrices) and are thesubject of several investigations into their existence in all dimensions.We often describe measurements by the vectors in Hilbert space ontowhich our operators project. In this sense, both contextual and symmetricmeasurements are connected to special sets of vectors. These vectors areoften special for another reason: they form congurations in a given incidencegeometry.In this thesis, we aim to show various connections between congurationsand measurements in quantum information. The congurations discussedhere would have been well-known to 19th and 20th century geometers andwe show they are relevant for advances in quantum theory today. Specically,the Hesse and Reye congurations provide proofs of measurement contextuality,both in its original form and its newer guise. The Hesse congurationalso ties together dierent types of symmetric measurements in dimension3called SICs and MUBswhile giving insights into the group theoreticalproperties of higher dimensional symmetric measurements.

Place, publisher, year, edition, pages
Department of Physics, Stockholm University , 2012. , 47 p.
National Category
Other Physics Topics
Research subject
Physics
Identifiers
URN: urn:nbn:se:su:diva-82921OAI: oai:DiVA.org:su-82921DiVA: diva2:573349
Opponent
Supervisors
Available from: 2012-11-30 Created: 2012-11-30 Last updated: 2013-02-28Bibliographically approved
List of papers
1. A Kochen-Specker inequality for a SIC
Open this publication in new window or tab >>A Kochen-Specker inequality for a SIC
2012 (English)In: Physics Letters A, ISSN 0375-9601, E-ISSN 1873-2429, Vol. 376, no 4, 374-376 p.Article in journal (Refereed) Published
Abstract [en]

Yu and Oh (eprint) [1] have given a state-independent proof of the Kochen–Specker theorem in three dimensions using only 13 rays. The proof consists of showing that a non-contextual hidden variable theory necessarily leads to an inequality that is violated by quantum mechanics. We give a similar proof making use of 21 rays that constitute aSIC (symmetric informationally-complete positive operator-valued measure) and a complete set of MUB (mutually unbiased bases). A theory-independent inequality is also presented using the same 21 rays, as required for experimental tests of contextuality.

Keyword
Kochen–Specker theorem, Non-contextuality, SIC and four MUB, Hesse configuration
National Category
Physical Sciences
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:su:diva-81909 (URN)10.1016/j.physleta.2011.12.011 (DOI)
Funder
Swedish Research Council
Available from: 2012-11-01 Created: 2012-11-01 Last updated: 2017-12-07Bibliographically approved
2. Proposed experiments of qutrit state-independent contextuality and two-qutrit contextuality-based nonlocality
Open this publication in new window or tab >>Proposed experiments of qutrit state-independent contextuality and two-qutrit contextuality-based nonlocality
Show others...
2012 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 85, no 3, 032108- p.Article in journal (Refereed) Published
Abstract [en]

Recent experiments have demonstrated ququart state-independent quantum contextuality and qutrit state-dependent quantum contextuality. So far, the most basic form of quantum contextuality pointed out by Kochen and Specker, and Bell, has eluded experimental confirmation. Here we present an experimentally feasible test to observe qutrit state-independent quantum contextuality using single photons in a three-path setup. In addition, we show that if the same measurements are performed on two entangled qutrits, rather than sequentially on the same qutrit, then the noncontextual inequality becomes a Bell inequality. We show that this connection also applies to other recently introduced noncontextual inequalities.

National Category
Physical Sciences
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:su:diva-76268 (URN)10.1103/PhysRevA.85.032108 (DOI)000301104400009 ()
Note

5

Available from: 2012-05-21 Created: 2012-05-10 Last updated: 2017-12-07Bibliographically approved
3. Mutually unbiased bases, Heisenberg-Weyl orbits and the distance between them
Open this publication in new window or tab >>Mutually unbiased bases, Heisenberg-Weyl orbits and the distance between them
2012 (English)Conference paper, Published paper (Other academic)
Abstract [en]

There is a famous construction of mutually unbiased bases in prime dimensions that uses the eigenbases of cyclic subgroups of the Heisenberg-Weyl group. Less well-known perhaps is that orbits under the same group also form sets of mutually unbiased bases. Regarded as points in a Grassmannian space, we find that the individual bases from different sets of mutually unbiased bases lie at regular, repeating distances from one another and we conjecture an analytical expression for these distances based on their status as 2-designs.

Place, publisher, year, edition, pages
American Institute of Physics (AIP), 2012
Series
AIP Conference Proceedings, ISSN 0094-243X ; 1508
Keyword
Mutually unbiased bases, Heisenberg-Weyl group
National Category
Physical Sciences
Identifiers
urn:nbn:se:su:diva-87986 (URN)10.1063/1.4773148 (DOI)
Conference
Quantum Theory: Reconsideration of Foundations 6
Available from: 2013-02-28 Created: 2013-02-28 Last updated: 2013-03-11Bibliographically approved

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