ANNUAL REPORT - MTA SzFKI

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entanglement one has to find methods that need few measurements. Moreover, in manyparticle systems typically the particles cannot be addressed individually. Thus these methods can only use collective measurements. We have been working on methods for entanglement detection under these circumstances. On the one hand, we participated in an experiment carried out at the Max Planck Institute for Quantum Optics, where a four-qubit quantum state was created with photons, and the methods developed were used for entanglement detection. On the other hand, we determined the complete set of generalized spin squeezing inequalities that can detect entanglement in many-particle experiments. Finally, we worked on other aspects of entanglement detection issues related to mixed state quantum computing, and local hidden variable models. We generalized the concept of recurrence probability (Pólya number) for d-dimensional unbiased quantum walks. A sufficient condition for a quantum walk to be recurrent was derived. As a by-product we have found a simple criterion for localisation of quantum walks. In contrast to classical walks, where the Pólya number is characteristic for the given dimension, the recurrence probability of a quantum walk depends in general on the topology of the walk, choice of the coin and the initial state. This allows to change the character of the quantum walk from recurrent to transient by altering the initial state. Nuclear motion in molecules. — dynamics and spectroscopy. – A technique has been developed which in principle allows the determination of the full rotational-vibrational eigenspectrum of triatomic molecules by treating the important singularities present in the triatomic rotational-vibrational kinetic energy operator given in Jacobi coordinates and the R, embedding. A generalized finite basis representation resulting in a nonsymmetric Hamiltonian matrix has been employed. The basis set to be used is obtained by taking the direct product of a 1-D DVR basis, related to R1, with a 5-D nondirect-product basis, the latter formed by coupling Bessel-DVR functions depending on the distance-type coordinate causing the singularity, associated Legendre polynomials depending on the Jacobi angle, and rotational functions depending on the three Euler angles. The robust implicitly restarted Arnoldi method within the ARPACK package is used for the determination of a number of eigenvalues of the nonsymmetric Hamiltonian matrix. The suitability of the proposed approach is shown by the determination of the rotationalvibrational energy levels of the ground electronic state of H-3(+) somewhat above its barrier to linearity. Convergence of the eigenenergies is checked by an alternative approach, employing a Hamiltonian expressed in Radau coordinates, a standard directproduct basis, and no treatment of the singularities. E-Mail: Péter Ádám János Asbóth Péter Domokos Aurél Gábris József Janszky Orsolya Kálmán Attila Kárpáti Zsolt Kis Tamás Kiss Mátyás Koniorczyk Zoltán Kurucz Dávid Nagy adam@szfki.hu asboth@optics.szfki.kfki.hu domokos@szfki.hu gabrisa@optics.szfki.kfki.hu janszky@szfki.hu kalman@szfki.hu, karpati@optics.szfki.kfki.hu zsolt@szfki.hu tkiss@optics.szfki.kfki.hu kmatyas@optics.szfki.kfki.hu kurucz@szfki.kfki.hu nagyd@optics.szfki.kfki.hu, 86
Viktor Szalay Gergely Szirmai Géza Tóth András Vukics viktor@szfki.hu szirmai@optics.szfki.kfki.hu toth@optics.szfki.kfki.hu, vukics@optics.szfki.kfki.hu Grants and international cooperations OTKA T049234 Quantum optical systems and applications in quantum informatics (J. Janszky, 2005-2008) OTKA T043079 Moving atoms and molecules in strongly-coupled radiation fields (P. Domokos, 2003-2007) OTKA NF68736 Cavity Quantum Electrodynamics of systems from few atoms to controlled ensembles (P. Domokos, 2007-2010) OTKA T045955 Theoretical methods to describe vibrational-rotational motion of molecules (V. Szalay, 2004-2007) OTKA T049234 Detection of multipartite entanglement in quantum optical systems (G. Tóth, 2006-2009) TéT, Hungarian-Czech Bilateral Intergovernmental S&T Cooperation (CZ-2/2005): Quantum information and entanglement in quantum optical networks (T. Kiss, 2006-2007) TéT, Hungarian-Spanish Bilateral Intergovernmental S&T Cooperation (ESP-17/2006): Quantum control (V. Szalay, 2007-2008) FP6 Marie Curie European Reintegration Grant of the European Commission (MERG-CT- 2005-029146 ): Detection of multipartite entanglement in quantum optical systems (G. Tóth, 2006-2007) Öveges József program: Qubit dynamics in quantum optical networks (T. Kiss, 2006- 2007) Öveges József program: Cavity Quantum Electrodynamics: from atoms to many-body systems (P. Domokos, 2006-2007) Publications Articles T.1. T.2. T.3. T.4. T.5. T.6. Gühne * O, Mechler * M, Tóth G, Adam P; Entanglement criteria based on local uncertainty relations are strictly stronger than the computable cross norm criterion; Phys Rev A; 74, 010301/1-4, 2006 Kiss T, Jex * I, Alber * G, Vymetal * S; Complex chaos in conditional qubit dynamics and purification; Acta Phys Hung B; 26, 229–235, 2006 Kurucz Z, Ádám P, Janszky J; Remote state preparation in quadrature basis; Acta Phys Hung B; 26, 319-326, 2006 Nagy D, Asbóth J, Domokos P; Collective cooling of atoms in a ring cavity; Acta Phys Hung B; 26, 141-148, 2006 Stefanak * M, Kiss T, Jex * I, Mohring * B; The meeting problem in the quantum walk; J Phys A; 39, 14965-14983, 2006 Almeida * ML, Pironio * S, Barrett * J, Tóth G, Acín * A; Noise robustness of the nonlocality of entangled quantum states; Phys Rev Lett; 99, 040403/1-4, 2007 87
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ANNUAL REPORT 2007 RESEARCH INSTITU
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Dear Reader, It is my pleasure to h
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Key figures Permanent staff of the
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A. STRONGLY CORRELATED SYSTEMS J. S
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presented detailed study should hel
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B. COMPLEX SYSTEMS F. Iglói, R. Ju
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B.3. B.4. B.5. B.6. B.7. B.8. B.9.
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the α2 reconstruction increases on
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C.2. C.3. Kádas K, Vitos L, Johans
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C.27. Ropo * M, Kokko * K, Punkkine
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I 25 4 3 Fig. 2. Average intensity
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See also H.6. and nanostructured Pd
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Ab initio structure solution. — I
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ESA PECS 98021 Phase field modeling
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Conference proceedings E.17. Oszlá
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Fig. 1. ns-EC to s-EC transition in
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Publications Articles F.1. F.2. Bö
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G. ELECTRON CRYSTALS G. Kriza, P. M
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