Geometric spin Hall effect of light is a fundamental phenomenon occurring when a polarized beam of light is observed from a reference frame tilted with respect to the direction of propagation of the beam. This effect has a purely geometric nature and amounts to a polarizationdependent shift/split of the beam intensity distribution evaluated as the time averaged flux of the Poynting vector across the plane of observation. This shift is unavoidable whenever the beam possesses a nonzero transverse angular momentum.
Quantum key distribution (QKD) is a procedure of information exchange between two parties, the sender Alice and the receiver Bob, which allows to distribute absolutely secure data between them. Currently, QKD is the most successful application of quantum information theory. The distinctive part of QKD with respect to classical communication is the use of a quantum information channel, where the signal is protected from unauthorized duplication. We are working on security analysis of existing QKD protocols, as well as developing new ones  more robust and more efficient. Especially we are interested in QKD with coherent states of light, which is experimentally implemented in our institute. References: [1] D. Sych and G. Leuchs, arXiv:0902.1895 (2009) [2] D. Elser, T. Bartley, B. Heim, C. Wittmann, D. Sych and G. Leuchs, New Journal of Physics, 11 (4), 045014 (2009)
Efficient coupling between light and matter at a single quantum level in free space lies at the heart of scalable quantum information processing, computation and communication. In our work we theoretically investigate a scheme for perfect excitation of a matter qubit by a single photon in free space. The experimental realization consists of a single twolevel ion trapped at the focus of a parabolic metallic mirror. We calculate the normal modes of the radiation field genuine to the parabolic geometry within the vectorial model of light by including the polarization degree of freedom and check the free space assumption for our setup. The parabolic shape of the mirror can mimic free space while allowing for full control over the field modes at the same time (see Fig. 1). Next, we calculate the radiation field uncertainties. The time evolution of the atomic excitation probability probes the dynamics of the uncertainties of the quantized radiation field in the immediate vicinity of the atom. The uncertainties of the radiation field far away from the atom reveal the characteristic shape of the timereversed dipole wave which leads to asymptotically perfect excitation. References: [1] M. Stobinska, G. Alber, and G. Leuchs, EPL 86, 14007 (2009) [2] M. Stobinska, R. Alicki, arXiv:0905.4014v1
Possibility of the macromacro entanglement generation has been recently proposed [F. De Martini, arXiv: 0903.1992] based on the phasecovariant quantum amplifiers. We study a simple preselection procedure for the macromacro entanglement which constitutes a novel type of polarization entanglement source. In particular, it overcomes both the detector efficiency and the welldefined local macroobservables problems. The preselection procedure directly leads to a loopholefree Bell inequality test experimentally feasible within the current technology. References: [1] M. Stobinska, P. Horodecki, R. Chhajlany, R. Horodecki, arXiv:0909.1545v1
Quantum computer (QC) consisting of 106 qubits and performing each operation with an error below 10^(6) will beat the classical computer in prime factorization problem. Quantum algorithms performed on it will provide us with exponential speedup of computation. Experimental realization of QC still remains challenging. Until today, all realizations based on trapped ions and cavity quantum electrodynamics (QED) suffer from technical limitations which make the scalability of the system, i.e. enlarging the setup without a significant effort, impossible. In our work we present a scalable system based on a single electron confined in a carbon nanotube quantum dot (see Fig. 2). The presence of an external static magnetic field along the tube axis provides the quantization axis for the electron spin and the orbital angular momentum. Thus, it provides us with two possible logical qubits. We discuss possible realizations of the universal set of quantum gates.
The simplest quantum translation of the classical formalism of polarization is associated with problems. For example, some quantum states that clearly depend on rotations of polarization will then be described as unpolarized. Several quantum degrees of polarization that take into account higherorder correlations have therefore been suggested, but all have limited use. In this project, we aim to improve the understanding and description of quantum polarization properties.
 We have reviewed the controversial concept of "classical entanglement" in optical beams by presenting a unified theory for different kinds of classically entangled light beams and further developed the concept by indicating several possible extensions [1].
 We have shown that an optical Bell test that combines discreteoutcome and continuousvariable measurements is remarkably tolerant against experimental imperfections when it is run with amplified twophoton N00N states [2].
 The mathematical structure of entanglement is present in the vectorial beams of classical optics. Applying quantuminformational concepts, we have found that radially polarized beams of light allow to perform realtime singleshot Mueller matrix polarimetry [3].
 Squeezedvacuum twin beams are known to have perfect photonnumber correlations and hence a huge phase uncertainty. By overlapping bright twin beams on a beam splitter, we have for the first time in optical beams observed the typical 'Ushape' of the output photonnumber distribution, manifesting the conversion of phase fluctuations into photonnumber fluctuations [4].
 We have studied the GoosHänchen and ImbertFedorov shifts by using a quantummechanical formalism. This approach furnished naturally a separation of the spatial shift into one part independent of orbital angular momentum (OAM) and another OAMdependend part. In addition, the proportionality of the angular shift and the beam’s angular spread became apparent [5].
 Considering pairs of indistinguishable particles under unitary transformations, occurring e.g. in random walks, we have found that the expectation value of an observable evaluated for identical classical particles is exactly the sum of expectation values determined for fermions and bosons, divided by two [6].
[1] Andrea Aiello, Falk Töppel, Christoph Marquardt, Elisabeth Giacobino and Gerd Leuchs, “Classical entanglement: Oxymoron or resource", arXiv:1409.0213 [quantph] (to appear in New J. Phys.)
[2] Falk Töppel and Magdalena Stobińska, “Robust test of Bell's inequality with amplified N00N states”, arXiv:1404.0867 [quantph]
[3] Falk Töppel, Andrea Aiello, Christoph Marquardt, Elisabeth Giacobino and Gerd Leuchs, “Classical entanglement in polarization metrology”, New J. Phys. 16, 073019 (2014)
[4] Kirill Yu. Spasibko, Falk Töppel, Timur Sh. Iskhakov, Magdalena Stobińska, Maria V. Chekhova and Gerd Leuchs, “Interference of macroscopic beams on a beam splitter: phase uncertainty converted into photonnumber uncertainty”, New J. Phys. 16, 013025 (2014)
[5] Falk Töppel, Marco Ornigotti and Andrea Aiello, “GoosHänchen and ImbertFedorov shifts from a quantummechanical perspective”, New J. Phys. 15, 113059 (2013)
[6] Falk Töppel and Andrea Aiello, “Identical classical particles: half fermions and half bosons”, Phys. Rev. A 88, 012130 (2013)
