Ändra sökning
RefereraExporteraLänk till posten
Permanent länk

Direktlänk
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Annat format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annat språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf
Exploring the Set of Quantum States
Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
2007 (Engelska)Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
Abstract [en]

Quantum mechanical properties of finite dimensional quantum systems are used within the field of quantum information. In this thesis the set of states (density matrices) for such systems is studied and described, largely in geometrical terms. The introductory part also acquaints the reader with relevant background about majorization, bistochastic matrices, mutually unbiased bases, Hadamard matrices and entanglement, with the aim to make the papers attached easier to read.

Paper I considers Peres' criterion for separability, for two qubit states. Paper II deals with the problem of how density matrices can be mixed from pure states, especially what probability distributions over pure states that are possible. In Paper III the set of bistochastic matrices–Birkhoff's polytope–and the subset of unistochastic matrices is studied, with a detailed description in dimensions 3 and 4. In Paper IV it is seen how the states of a complete set of mutually unbiased bases form a polytope in the set of density matrices, with certain combinatorial properties. A search for mutually unbiased bases in dimension 6 is presented in Paper VI, which includes a thorough discussion on 6 by 6 Hadamard matrices. Paper V presents a result about geodesics in the set of quantum states with respect to the curved Bures-Uhlmann geometry.

Ort, förlag, år, upplaga, sidor
Stockholm: Fysikum , 2007. , 82 s.
Nyckelord [en]
quantum mechanics, quantum states, density matrices, quantum information, geometry
Nationell ämneskategori
Fysik
Forskningsämne
teoretisk fysik
Identifikatorer
URN: urn:nbn:se:su:diva-6993ISBN: 978-91-7155-475-8 (tryckt)OAI: oai:DiVA.org:su-6993DiVA: diva2:197433
Disputation
2007-09-17, sal FB42, AlbaNova universitetscentrum, Roslagstullsbacken 21, Stockholm, 13:00
Opponent
Handledare
Tillgänglig från: 2007-08-15 Skapad: 2007-08-15Bibliografiskt granskad
Delarbeten
1. Separability and the stella octangula
Öppna denna publikation i ny flik eller fönster >>Separability and the stella octangula
2002 Ingår i: Physics Letters A, ISSN 0375-9601, Vol. 295, nr 5-6, 256-258 s.Artikel i tidskrift (Refereegranskat) Published
Identifikatorer
urn:nbn:se:su:diva-24387 (URN)
Anmärkning
Part of urn:nbn:se:su:diva-6993Tillgänglig från: 2007-08-15 Skapad: 2007-08-15Bibliografiskt granskad
2. How to mix a density matrix
Öppna denna publikation i ny flik eller fönster >>How to mix a density matrix
2003 Ingår i: Physical Review A, ISSN 1050-2947, Vol. 67, 012107- s.Artikel i tidskrift (Refereegranskat) Published
Identifikatorer
urn:nbn:se:su:diva-24388 (URN)
Anmärkning
Part of urn:nbn:se:su:diva-6993Tillgänglig från: 2007-08-15 Skapad: 2007-08-15Bibliografiskt granskad
3. Birkhoff’s Polytope and Unistochastic Matrices, N = 3 and N = 4
Öppna denna publikation i ny flik eller fönster >>Birkhoff’s Polytope and Unistochastic Matrices, N = 3 and N = 4
Visa övriga...
2005 Ingår i: Communications in mathematical physics, ISSN 0010-3616, Vol. 259, nr 2, 307-324 s.Artikel i tidskrift (Refereegranskat) Published
Identifikatorer
urn:nbn:se:su:diva-24389 (URN)
Anmärkning
Part of urn:nbn:se:su:diva-6993Tillgänglig från: 2007-08-15 Skapad: 2007-08-15Bibliografiskt granskad
4. Mutually unbiased bases and the complementarity polytope
Öppna denna publikation i ny flik eller fönster >>Mutually unbiased bases and the complementarity polytope
2005 Ingår i: Open systems & information dynamics, ISSN 1230-1612, Vol. 12, 107-120 s.Artikel i tidskrift (Refereegranskat) Published
Identifikatorer
urn:nbn:se:su:diva-24390 (URN)
Anmärkning
Part of urn:nbn:se:su:diva-6993Tillgänglig från: 2007-08-15 Skapad: 2007-08-15Bibliografiskt granskad
5. Geodesics and the best measurement for distinguishing quantum states
Öppna denna publikation i ny flik eller fönster >>Geodesics and the best measurement for distinguishing quantum states
2005 Ingår i: Journal of physics. A, Mathematical and general, ISSN 0305-4470, Vol. 38, L725-L730 s.Artikel i tidskrift (Refereegranskat) Published
Identifikatorer
urn:nbn:se:su:diva-24391 (URN)
Anmärkning
Part of urn:nbn:se:su:diva-6993Tillgänglig från: 2007-08-15 Skapad: 2007-08-15Bibliografiskt granskad
6. Mutually unbiased bases and Hadamard matrices of order six
Öppna denna publikation i ny flik eller fönster >>Mutually unbiased bases and Hadamard matrices of order six
Visa övriga...
2007 (Engelska)Ingår i: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 48, nr 5, 052106- s.Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

We report on a search for mutually unbiased bases (MUBs) in six dimensions. We find only triplets of MUBs, and thus do not come close to the theoretical upper bound 7. However, we point out that the natural habitat for sets of MUBs is the set of all complex Hadamard matrices of the given order, and we introduce a natural notion of distance between bases in Hilbert space. This allows us to draw a detailed map of where in the landscape the MUB triplets are situated. We use available tools, such as the theory of the discrete Fourier transform, to organize our results. Finally, we present some evidence for the conjecture that there exists a four dimensional family of complex Hadamard matrices of order 6. If this conjecture is true the landscape in which one may search for MUBs is much larger than previously thought.

Nationell ämneskategori
Fysik
Identifikatorer
urn:nbn:se:su:diva-24392 (URN)10.1063/1.2716990 (DOI)000246892400006 ()
Tillgänglig från: 2007-08-15 Skapad: 2007-08-15 Senast uppdaterad: 2013-05-02Bibliografiskt granskad

Open Access i DiVA

Fulltext saknas

Av organisationen
Fysikum
Fysik

Sök vidare utanför DiVA

GoogleGoogle Scholar

Totalt: 1165 träffar
RefereraExporteraLänk till posten
Permanent länk

Direktlänk
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Annat format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annat språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf