| 1. |
- Azimi Mousolou, Vahid, et al.
(författare)
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Non-Abelian geometric phases in a system of coupled quantum bits
- 2014
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Ingår i: Physical Review A. Atomic, Molecular, and Optical Physics. - 1050-2947 .- 1094-1622. ; 89:2, s. 022117-
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Tidskriftsartikel (refereegranskat)abstract
- A common strategy to measure the Abelian geometric phase for a qubit is to let it evolve along an `orange slice' shaped path connecting two antipodal points on the Bloch sphere by two different semi-great circles. Since the dynamical phases vanish for such paths, this allows for direct interference measurement of the geometric phase. Here, we generalize the orange slice setting to the non-Abelian case. The proposed method to measure the non-Abelian geometric phase can be implemented in a cyclic chain of four qubits with controllable nearest-neighbor interactions.
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| 2. |
- Azimi Mousolou, Vahid, et al.
(författare)
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Non-Abelian off-diagonal geometric phases in nano-engineered four-qubit systems
- 2013
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Ingår i: Europhysics letters. - : IOP Publishing. - 0295-5075 .- 1286-4854. ; 103:6, s. 60011-
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Tidskriftsartikel (refereegranskat)abstract
- The concept of off-diagonal geometric phase (GP) has been introduced in order to recover interference information about the geometry of quantal evolution where the standard GPs are not well-defined. In this Letter, we propose a physical setting for realizing non-Abelian off- diagonal GPs. The proposed non-Abelian off-diagonal GPs 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 GP.
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| 3. |
- Azimi Mousolou, Vahid, et al.
(författare)
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Non-Abelian quantum holonomy of hydrogen-like atoms
- 2011
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Ingår i: Physical Review A. Atomic, Molecular, and Optical Physics. - 1050-2947 .- 1094-1622. ; 84:3
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Tidskriftsartikel (refereegranskat)abstract
- We study the Uhlmann holonomy [Rep. Math. Phys. 24, 229 (1986)] of quantum states for hydrogen-like atoms, where the intrinsic spin and orbital angular momentum are coupled by the spin-orbit interaction and subject to a slowly varying magnetic field. We show that the holonomy for the orbital angular momentum and spin subsystems is non-Abelian, while the holonomy of the whole system is Abelian. Quantum entanglement in the states of the whole system is crucially related to the non-Abelian gauge structure of the subsystems. We analyze the phase of the Wilson loop variable associated with the Uhlmann holonomy, and find a relation between the phase of the whole system with corresponding marginal phases. Based on the result for the model system we provide evidence that the phase of the Wilson loop variable and the mixed-state geometric phase [Phys. Rev. Lett. 85, 2845 (2000)] are in general inequivalent.
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| 4. |
- Azimi Mousolou, Vahid, 1982-
(författare)
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Quantum Holonomy for Many-Body Systems and Quantum Computation
- 2013
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- 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 be comes 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.
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| 5. |
- Azimi Mousolou, Vahid, et al.
(författare)
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Unifying Geometric Entanglement and Geometric Phase in a Quantum Phase Transition
- 2013
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Ingår i: Physical Review A. Atomic, Molecular, and Optical Physics. - 1050-2947 .- 1094-1622. ; 88:1, s. 012310-
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Tidskriftsartikel (refereegranskat)abstract
- 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-value 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.
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| 6. |
- Azimi Mousolou, Vahid, et al.
(författare)
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Universal Non-adiabatic Holonomic Gates in Quantum Dots and Single-Molecule Magnets
- 2014
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Ingår i: New Journal of Physics. - : IOP Publishing. - 1367-2630. ; 16
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Tidskriftsartikel (refereegranskat)abstract
- Geometric manipulation of a quantum system offers a method for fast, universal, and robust quantum information processing. Here, we propose a scheme for universal all-geometric quantum computation using non-adiabatic quantum holonomies. We propose three different realizations of the scheme based on an unconventional use of quantum dot and single-molecule magnet devices, which offer promising scalability and robust efficiency.
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| 7. |
- Blanchfield, Kate
(författare)
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Configurations in Quantum Information
- 2012
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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| 8. |
- Ericsson, Marie, et al.
(författare)
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Comment on `Detecting non-Abelian geometric phases with three-level Λ systems'
- 2013
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Ingår i: Physical Review A. Atomic, Molecular, and Optical Physics. - 1050-2947 .- 1094-1622. ; 87:3, s. 036101-
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Tidskriftsartikel (refereegranskat)abstract
- In their recent paper, Yan-Xiong Du {\it et al.} [Phys. Rev. A {\bf 84}, 034103 (2011)] claim to have found a non-Abelian adiabatic geometric phase associated with the energy eigenstates of a large-detuned $\Lambda$ three-level system. They further propose a test to detect the non-commutative feature of this geometric phase. On the contrary, we show that the non-Abelian geometric phase picked up by the energy eigenstates of a $\Lambda$ system is trivial in the adiabatic approximation, while, in the exact treatment of the time evolution, this phase is very small and cannot be separated from the non-Abelian dynamical phase acquired along the path in parameter space.
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| 9. |
- Johansson, Markus, et al.
(författare)
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Classification scheme of pure multipartite states based on topological phases
- 2014
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Ingår i: Physical Review A. Atomic, Molecular, and Optical Physics. - 1050-2947 .- 1094-1622. ; 89:1, s. 012320-
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Tidskriftsartikel (refereegranskat)abstract
- We investigate the connection between the concept of a-balancedness introduced in [Phys. Rev A. 85, 032112 (2012)] and polynomial local SU invariants and the appearance of topological phases respectively. It is found that different types of a-balancedness correspond to different types of local SU invariants analogously to how different types of balancedness as defined in [New J. Phys. 12, 075025 (2010)] correspond to different types of local SL invariants. These different types of SU invariants distinguish between states exhibiting different topological phases. In the case of three qubits the different kinds of topological phases are fully distinguished by the three-tangle together with one more invariant. Using this we present a qualitative classification scheme based on balancedness of a state. While balancedness and local SL invariants of bidegree $(2n,0)$ classify the SL-semistable states [New J. Phys. 12, 075025 (2010), Phys. Rev. A 83, 052330 (2011)], a-balancedness and local SU invariants of bidegree (2n-m,m) gives a more fine grained classification. In this scheme the a-balanced states form a bridge from the genuine entanglement of balanced states, invariant under the SL-group, towards the entanglement of unbalanced states characterized by U invariants of bidegree (n,n). As a by-product we obtain generalizations to the W-state, states that are entangled, but contain only globally distributed entanglement of parts of the system.
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| 10. |
- Johansson, Markus, et al.
(författare)
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Correlation-induced non-Abelian quantum holonomies
- 2011
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Ingår i: Journal of Physics A. - : IOP Publishing. - 0305-4470 .- 1361-6447. ; 44:14, s. 145301-
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Tidskriftsartikel (refereegranskat)abstract
- In the context of two-particle interferometry, we construct a parallel transport condition that is based on the maximization of coincidence intensity with respect to local unitary operations on one of the subsystems. The dependence on correlation is investigated and it is found that the holonomy group is generally non-Abelian, but Abelian for uncorrelated systems. It is found that our framework contains the Lévay geometric phase (2004 J. Phys. A: Math. Gen. 37 1821) in the case of two-qubit systems undergoing local SU(2) evolutions.
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