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Global asymmetry of many-qubit correlations: A lattice-gauge-theory approach
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)
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2011 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 84, no 3, 032302- p.Article in journal (Refereed) Published
Abstract [en]

We introduce a novel bridge between the familiar gauge field theory approaches used in many areas of modern physics such as quantum field theory and the SLOCC protocols familiar in quantum information. Although the mathematical methods are the same the meaning of the gauge group will be different. The measure we introduce, `twist', is constructed as a Wilson loop from a correlation induced holonomy. The measure can be understood as the global asymmetry of the bipartite correlations in a loop of three or more qubits; if the holonomy is trivial (the identity matrix), the bipartite correlations can be globally untwisted using general local qubit operations, the gauge group of our theory, which turns out to be the group of Lorentz transformations familiar from special relativity. If it is not possible to globally untwist the bipartite correlations in a state globally using local operations, the twistedness is given by a non-trivial element of the Lorentz group, the correlation induced holonomy. We provide several analytical examples of twisted and untwisted states for three qubits, the most elementary non-trivial loop one can imagine.

Place, publisher, year, edition, pages
2011. Vol. 84, no 3, 032302- p.
Keyword [en]
Multiparticle quantum correlations, lattice gauge theory, Minkowski space-time, holonomy
National Category
Physical Sciences
Research subject
Physics and Astronomy specializing in Theoretical Physics
Identifiers
URN: urn:nbn:se:uu:diva-149238DOI: 10.1103/PhysRevA.84.032302ISI: 000294470300003OAI: oai:DiVA.org:uu-149238DiVA: diva2:404106
Funder
Swedish Research Council
Note

Additional address (M.S. Williamson): Erwin Schrödinger International Institute for Mathematical Physics. Additional address (E. Sjöqvist): Centre for Quantum Technologies, NUS, Singapore. Additional address (V. Vedral): Clarendon Laboratory, University of Oxford, UK; Also in Virtual Journal of Quantum Information, September issue 2011 and Virtual Journal of Nanoscale Science and Technology, September 19 issue 2011

Available from: 2011-03-16 Created: 2011-03-16 Last updated: 2017-12-11Bibliographically approved

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Ericsson, MarieJohansson, MarkusSjöqvist, Erik

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