uu.seUppsala University Publications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Geometric local invariants and pure three-qubit states
Centre for Quantum Technologies, NUS, Singapore.
Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Physical and Analytical Chemistry, Quantum Chemistry. (Quantum information theory)
Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Physical and Analytical Chemistry, Quantum Chemistry. (Quantum information theory)
Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Physical and Analytical Chemistry, Quantum Chemistry. (Quantum information theory)
Show others and affiliations
2011 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 83, no 6, 062308Article in journal (Refereed) Published
Abstract [en]

We explore a geometric approach to generating local SU(2) and SL(2,C) invariants for a collection of qubits inspired by lattice gauge theory. Each local invariant or 'gauge' invariant is associated to a distinct closed path (or plaquette) joining some or all of the qubits. In lattice gauge theory, the lattice points are the discrete space-time points, the transformations between the points of the lattice are defined by parallel transporters and the gauge invariant observable associated to a particular closed path is given by the Wilson loop. In our approach the points of the lattice are qubits, the link-transformations between the qubits are defined by the correlations between them and the gauge invariant observable, the local invariants associated to a particular closed path are also given by a Wilson loop-like construction. The link transformations share many of the properties of parallel transporters although they are not undone when one retraces one's steps through the lattice. This feature is used to generate many of the invariants. We consider a pure three qubit state as a test case and find we can generate a complete set of algebraically independent local invariants in this way, however the framework given here is applicable to mixed states composed of any number of d level quantum systems. We give an operational interpretation of these invariants in terms of observables.

Place, publisher, year, edition, pages
2011. Vol. 83, no 6, 062308
Keyword [en]
Lattice gauge theory, local invariants, quantum entanglement
National Category
Physical Sciences
Research subject
Physics
Identifiers
URN: urn:nbn:se:uu:diva-147858DOI: 10.1103/PhysRevA.83.062308ISI: 000291351400004OAI: oai:DiVA.org:uu-147858DiVA: diva2:400974
Funder
Swedish Research Council
Available from: 2011-03-09 Created: 2011-02-28 Last updated: 2017-12-11Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full textarxiv/1102.4222

Authority records BETA

Ericsson, MarieJohansson, MarkusSjöqvist, Erik

Search in DiVA

By author/editor
Ericsson, MarieJohansson, MarkusSjöqvist, Erik
By organisation
Quantum Chemistry
In the same journal
Physical Review A. Atomic, Molecular, and Optical Physics
Physical Sciences

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 936 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf