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Unifying geometric entanglement and geometric phase in a quantum phase transition
Linnaeus University, Faculty of Technology, Department of Physics and Electrical Engineering. (Condensed Matter Physics)
Linnaeus University, Faculty of Technology, Department of Physics and Electrical Engineering. (Condensed Matter Physics)ORCID iD: 0000-0003-4489-7561
Department of Quantum Chemistry, Uppsala University, Box 518, Se-751 20 Uppsala, Sweden.
2013 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 88, no 1, Article ID: 012310- p.Article in journal (Refereed) Published
Abstract [en]

Geometric measure of entanglement and geometric phase have recently been used to analyze quantum phase transition in the XY spin chain. We unify these two approaches by showing that the geometric entanglement and the geometric phase are respectively the real and imaginary parts of a complex-valued geometric entanglement, which can be investigated in typical quantum interferometry experiments. We argue that the singular behavior of the complex-valued geometric entanglement at a quantum critical point is a characteristic of any quantum phase transition, by showing that the underlying mechanism is the occurrence of level crossings associated with the underlying Hamiltonian.

Place, publisher, year, edition, pages
2013. Vol. 88, no 1, Article ID: 012310- p.
National Category
Condensed Matter Physics
Research subject
Physics, Condensed Matter Physics
Identifiers
URN: urn:nbn:se:lnu:diva-28081DOI: 10.1103/PhysRevA.88.012310ISI: 000321833000004Scopus ID: 2-s2.0-84880606305OAI: oai:DiVA.org:lnu-28081DiVA: diva2:640241
Available from: 2013-08-13 Created: 2013-08-13 Last updated: 2017-12-06Bibliographically approved
In thesis
1. Quantum Holonomy for Many-Body Systems and Quantum Computation
Open this publication in new window or tab >>Quantum Holonomy for Many-Body Systems and Quantum Computation
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The research of this Ph. D. thesis is in the field of Quantum Computation and Quantum

Information. A key problem in this field is the fragile nature of quantum states. This

becomes increasingly acute when the number of quantum bits (qubits) grows in order to

perform large quantum computations. It has been proposed that geometric (Berry) phases

may be a useful tool to overcome this problem, because of the inherent robustness of such

phases to random noise. In the thesis we investigate geometric phases and quantum

holonomies (matrix-valued geometric phases) in many-body quantum systems, and elucidate

the relationship between these phases and the quantum correlations present in the systems.

An overall goal of the project is to assess the feasibility of using geometric phases and

quantum holonomies to build robust quantum gates, and investigate their behavior when the

size of a quantum system grows, thereby gaining insights into large-scale quantum

computation.

In a first project we study the Uhlmann holonomy of quantum states for hydrogen-like

atoms. We try to get into a physical interpretation of this geometric concept by analyzing its

relation with quantum correlations in the system, as well as by comparing it with different

types of geometric phases such as the standard pure state geometric phase, Wilczek-Zee

holonomy, Lévay geometric phase and mixed-state geometric phases. In a second project we

establish a unifying connection between the geometric phase and the geometric measure of

entanglement in a generic many-body system, which provides a universal approach to the

study of quantum critical phenomena. This approach can be tested experimentally in an

interferometry setup, where the geometric measure of entanglement yields the visibility of

the interference fringes, whereas the geometric phase describes the phase shifts. In a third

project we propose a scheme to implement universal non-adiabatic holonomic quantum

gates, which can be realized in novel nano-engineered systems such as quantum dots,

molecular magnets, optical lattices and topological insulators. In a fourth project we propose

an experimentally feasible approach based on “orange slice” shaped paths to realize non-

Abelian geometric phases, which can be used particularly for geometric manipulation of

qubits. Finally, we provide a physical setting for realizing non-Abelian off-diagonal

geometric phases. The proposed setting can be implemented in a cyclic chain of four qubits

with controllable nearest-neighbor interactions. Our proposal seems to be within reach in

various nano-engineered systems and therefore opens up for first experimental test of the

non-Abelian off-diagonal geometric phase.

Place, publisher, year, edition, pages
Växjö: Linnaeus University Press, 2013. 140 p.
Series
Linnaeus University Dissertations, 141/2013
Keyword
Quantum holonomy, geometric phase, quantum correlations, quantum phase transitions, quantum computation
National Category
Condensed Matter Physics Other Physics Topics
Research subject
Natural Science; Natural Science, Physics
Identifiers
urn:nbn:se:lnu:diva-28311 (URN)978-91-87427-38-1 (ISBN)
Public defence
2013-08-26, Ny227, Kalmar Nyckel, Kalmar, 13:00 (English)
Opponent
Supervisors
Available from: 2013-09-10 Created: 2013-08-21 Last updated: 2013-09-10Bibliographically approved

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Azimi Mousolou, VahidCanali, Carlo M.

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