ANNUAL REPORT - MTA SzFKI

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,
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