Silvia Bergamini ``Experiment in a micro-dipole trap''
      There is currently a strong interest for the manipulation of neutral atoms. The manipulation of individual quantum objects opens the way to controlled engineering of the quantum state of a small set of trapped particles, in order to encode and process information at the quantum level. Our setup is capable of confining atoms to a micrometer sized region. The reduced volume of the trapping region allows to restrict the number of stored atoms: in particular, by carefully choosing the loading rate, it is possible to load the trap in the "collisional blocade" regime. In this regime only one atom at the time can be trapped in the dipole potential. The versatility of the experiment and the efficacity of the imaging system allow the manipulation and detection of a single atom or the loading of a controlled small number of atoms (10-20).
      The capability of addressing and detecting a single atom is paricularly favorable for studying way of manipulating the quantum state of the atom, as a method for qubits encoding. At the moment we are implementing experiments aimed at controlling the hyperfine state of the atom (RF driving of hyperfine transitions) as well as the motional state (Sideband-Raman Cooling).
      Experiments in the N-atoms regime are being implemented at the same time, aiming at placing all the atoms in the ground vibrational state of the dipole potential, in view of preparing a Bose-Einstein condensate with a very small number of atoms confined to the nanometer scale. Some preliminary tests have been made, which show the efficiency of evaporative cooling in our setup. Further cooling can also be obtained via sideband-Raman cooling. The nano-BEC could then be used to implement an N-qubits register, by creating an array of atoms in the ground vibrational state of an optical lattice (Mott transition).

Jan Bouda ``Classical and quantum cryptography''
      This talk will present basic definitions of perfect security of both classical and quantum cryptosystems. The practical problems and differences will be discussed. It will also give a brief introduction to the quantum cryptography with stress put on the main goals of the quantum cryptography.

Caslav Brukner ``What are the Bell innequalities good for?''
      It is widely accepted that violation of Bells inequalities is simply a witness of non-separability, and not even a very good one. The aim of this talk is to show that this is too narrow and simplistic opinion. As an explicite example a class of multi-party communication complexity problems will be considered. It will be shown that problems from that class can be solved in a protocol assisted by entangled states with higher efficiency than using any classical strategy if and only if the state violates a Bell inequality. This suggets a new significance for Bell's inequalities.

Vladimír Bužzek ``From flipping qubits to quantum programming''
      Coherent control over individual quantum systems is one of the most exciting achievements in physics in the last decade. The possibility to control quantum dynamics has far reaching consequences for quantum technologies, and in particular for quantum computing.
      In this lecture I will describe how information encoded in quantum systems can be manipulated. In particular, I will address the problem of flipping of qubits by using the universal NOT gate. I will show that this gate can also be used as a programmable quantum processor which would allow us to simulate completely positive maps (i.e. quantum mechanical processes) on quantum systems. Programmable quantum processors have two registers, the data register and the program register. The data register is a quantum system on which the map (i.e. a specific dynamics) is going to be applied. In the program register the information about the dynamics itself is encoded. The virtue of this arrangement is that we do not have to build a different processor every time we want to realize a new map.

Benoit Darquie ``Manipulation of single atoms''
      Neutral atoms offer a possible way for implementation of quantum gates. As a step in this direction, we describe the implementation of a microscopic dipole trap realized by using a sharply focused laser beam. The experiment is designed to allow to address individual atoms. The experimental set-up consists basically of a rubidium 87 Magneto-Optical Trap (MOT), in the center of which a red detuned beam is focused down to a very small spot size (beam waist less than 1 micron), in order to create an optical dipole trap. We are able to experimentally trap a single atom into a microscopic dipole trap. Further experiments require the atom to be in the ground state of the potential well, or at least in the Lambe-Dicke regime. It is thus of primary importance to know the temperature of the trapped atom and the oscillation frequencies of the trap . We show how it has been possible to measure these parameters, and what are the consequences for future experiments.

J. P. Home ``Loading and Trapping of Ions for Quantum Information Processing
      We are developing quantum information experiments in an ion trap. In the first phase of the project we have used magnetic sub-levels of the ground state of Calcium 40 as qubit levels. More recently we have begun to explore the experimental issues involved in using hyperfine structure of the ground state of Calcium 43. We have recently demonstrated two-stage photoionization of Calcium, leading to isotope selective loading of ions. Using this technique, we have loaded single Calcium 43 ions and a three ion crystal. We are currently investigating the loading process in more detail. The talk will also discuss some other experimental issues, in particular the need to increase the trap tightness and reduce electric field noise. To this end we have built a helical core quarter-wave resonator to replace our A.C. electrode power supply.

Derek Mc Hugh ``Quantum Computation with Ion Trap Spin Molecules''
      This talk will present the idea of quantum computing with cold, trapped ions in the presence of a magnetic field gradient. The differences between this and current quantum computer implementations will be discussed.

Matyás Koniorczik "Stabilizing optical qubits via squeezing"
      The robustness against loss of quantum states describing an actual realization of qubits is an important question in any particular case. The term "robustness" may be understood several ways in this context.
      In our work optical modes are considered. A simple model of loss is utilized, namely the interference of the mode representing a qubit with another mode representing the "environment" on a nearly transparent beam-splitter. The analysis is focused on the behavior of two orthogonal states, which are both superpostions of two coherent states, i.e. orthogonal Schrödinger-cats, representing the computational basis. The analysis can easily be extended to any other pair of orthogonal states.
      As a minimal requirement on the computational basis one may examine whether its elements are distinguishable in a few measurements, and thus support at least classical communication. We have chosen the quantum relative entropies as a measure of distinguishability: according to quantum Sanov theorem, the larger this quantity is, the less measurements are required in order to distinguish between the two states. Schrödinger cats are utmost fragile states, they are quickly "killed" by loss. However, the preparation of the environment in a suitable state may protect them, they may become stabilized against loss.
      We present the results of numerical calculations revealing the behavior of Schrödinger cats and certain other states when the auxiliary mode is in a squeezed state. We show that certain Schrödinger-cats can be indeed stabilized.

Jozef Košík ``Quantum random walks''
      Quantum random walks have been investigated in connection with the search for new quantum algorithms. They have some striking differences in comparison with classical random walks: they exhibit quadratic, or even exponential speedup over their classical counterparts, depending on the underlying graph, with respect to various measures. We examine the QRWs on the cycle and hypercube and show how the speedup is achieved, and moreover we propose an alternative model of quantum random walk, based on the local spin interaction, similar to the Ising type interaction.

Paolo Maioli ``Non-demolition measurement of a single atom
      We have tested the creation and annihilation of a microwave field inside a high-Q cavity using a technique reminiscent of homodyne measurement in laser optics. The same coherent field is injected twice in the cavity with a precise phase relation between the two injections; a two state atom prepared in the lower energy state and interacting resonantly with the cavity mode measures the remaining field by absorption. When the two injected fields have opposite phases, the final field cancels out, resulting in no absorption by the atom. By sending a dephasing atom between the two injections, we are able to detect its presence through the phase shift it produces on the field inside the cavity via a dispersive interaction. This realises a non demolition measurement of a single flying atom. Generation and detection of Shr\"odinger cat states by resonant interaction will be discussed.

Daniel Nagaj ``Quantum Homogenization via Beam Splitters''
      Quantum homogenization is a process, where a signal state is homogenized towards a reservoir state via many small interactions in a reservoir. A particular optical realization of this process - a beam splitter array - is discussed. We find the process is reversible and that the information about the input state is encoded into entanglement between the states involved. The separability of the states is analyzed using Simon's criterion.

Eoin Phillips ``Doppler cooling and axialisation of ions in a Penning trap"
      Most research into the use of trapped ions for quantum information processing (QIP) has focused on ions in Paul and linear RF traps. There is evidence to suggest, however, that the Penning trap might also be a good candidate for QIP. Large, static, electric and magnetic fields are used to trap the ion, which reduces the problem of stray fields affecting the trapped particle. Other advantages include the use of larger electrodes, reducing the impact of patch potentials on the experiment.
      Although single ions have been routinely prepared in a Penning trap, they are not as well localised as ions in an RF trap due to the difficulty in cooling the magnetron motion. The technique of axialisation [Phys Rev Lett 89 93003 (2002)], where the magnetron and modified cyclotron motions are coupled by a radial quadrupole field allows for efficient damping of the magnetron motion and good localisation of the ion. Evidence for this has been obtained through imaging of the ion and the comparison of damping rates with and without axialisation.
      Work on the axialisation of Mg$^+$ ions is presented, including demonstration of the increased damping rates with the use of the axialisation technique. Current work on the Doppler cooling of Ca$^+$ ions in a Penning trap is also discussed, with consideration of some technical differences compared to cooling in an RF trap.

Martin Plesch ``Entangled graphs''
      We stydy the problem of many-particle entanglement. We try to characterize a pure state of many qubits with the help of bipartite entanglement between all possible pairs. With the help of an ``entangled graph'', which represents the bipartite entanglement properties of a state in the graph, we try to gain a new view on the problem. In entangled graph each particle is represented a s a vertex and entanglement between a pair of qubits is represented as an edge between two vertices. These edges are inoriented, but can be wighted by concurrence.
      The second part will be devoted to classical correlations. We introduce new type of edge to our graphs, the classical correlation edge (broken line), i.e. the number of possible graphs increase. In particular, we are interested in pure state representation of these graphs.

Marco Ricci "Pauli tomography of a single qubit device"
      In the framework of quantum computation Tomography represents a useful task to characterize quantum states and operators. Exploiting the parallelism of entanglement we derive a simple way to implement quantum process tomography. Moreover we present the experimental realization of a Pauli tomography of a single qubit device, where the qubits are encoded in the polarization of a single photon.

Peter Štelmachovič ``On the role of initial correlations and complete positivity''
      The condition of complete positivity is one of the conditions any quantum dynamical map is supposed to satisfy. The Kraus representation theorem states that if an evolution is completely positive (and linear) then the evolution can be realized as an evolution of a subsystem of a larger system with no initial correlations. On the other hand we cannot prevent a quantum system as well as a preparation device from interacting with their environment. Thus in general, an initial state is not factorised and we can expect a presence of initial correlations. We discuss the role of initial correlations in the dynamics of open systems and its relation to the condition of complete positivity.

S.C.Webster ``Determining the angular momentum of the ground state of $^{40}$Ca$^+$''
      We are working on methods of determining the angular momentum of the ground state of the $^{40}$Ca$^+$ ion. This will then allow us to use the two Zeeman sublevels of the ground state for the storage and manipulation of quantum information. To perform readout of the state, an electron shelving method is used. The population in the $4S^{-1/2}_{1/2}$ qubit state is transferred to the metastable $3D_{5/2}$ `shelf' level. We can then detect if the ion is still in the ground state (i.e. in the other qubit state, $4S^{+1/2}_{1/2}$ ) by driving the $4S_{1/2} \to 4P_{1/2}$ transition and looking for fluorescence. In all the methods we have investigated population is not directly transferred into the shelf from the $4S^{-1/2}_{1/2}$ sublevel but instead to the $4P_{3/2}$ level, from where it can then decay into the shelf. We have tried three methods of achieving this.
      The first is direct excitation from $4S^{-1/2}_{1/2}\to 4P^{-3/2}_{3/2}$ with 393 nm $\sigma{-}$ light. This requires a magnetic field to be applied which produces a Zeeman splitting large compared with the 23 MHz natural linewidth, so as to make excitation from $4S^{+1/2}_{1/2}$ small. This method works, however the comparatively large magnetic field required makes it unsuitable for use in quantum information processing. The other two methods make use of two photon effects to produce good readout efficiency at low magnetic fields. The `bright resonance' method uses intense off-resonant light on the $3D_{3/2}$ to $4P_{3/2}$ transition to create a resonance narrower than the 23 MHz width of the direct excitation method, allowing it to be used at lower fields. The `EIT' or `dark resonance' method uses intense onresonant light on the $3D_{3/2} \to 4P_{3/2}$ transition to supress unwanted excitation from the $4S^{+1/2}_{1/2}$ qubit state.
      All three methods have been investigated theoretically and experimentally.

Tatjana Wilk ``Single photons for optical quantum computing''
      Knill, Laflamme and Milburn have proposed a quantum-information processing scheme with single-photons and linear optics [E. Knill, R. Laflamme and J. Milburn, Nature 409, 46 (2001)]. This scheme requires indistinguishable photons, since the proposed quantum-gates are based on perfect second-order interference. A Hong-Ou-Mandel type experiment [C. K. Hong, Z. Y. Ou and L. Mandel, Phys. Rev. Lett. 59, 2044 (1987)] will show whether the single-photon source realised in our group [M. Hennrich et al, Phys. Rev. Lett. 85, 4872 (2000), A. Kuhn et al, Phys. Rev. Lett. 89, 067901 (2002)] meets these conditions.
      Two photons, which are indistinguishable in their spatial, temporal, spectral and polarization modes, and which are superposed on a beam splitter, will always leave the beam splitter in the same direction. Hence detectors that monitor the two output ports of the beam splitter will never show coincidence counts if the photons match each other. Note that coincidences occure if the photons can be distinguished. Therefore, this method is used to determine the degree of mutual coherence between photons. The number of coincidence counts is a measure for the mismatch of the photonic modes.
      In our experiment, single-photons are generated individually by a triggered cavity-QED source with an adjustable delay. Subsequent photons are directed along paths of different length so that they arrive simultaneously at the 50:50 beam splitter. In contrast to preceding experiments [H. de Riedmatten et al, Phys. Rev. A 67, 022301 (2003) Ch. Santori et al, Nature 419, 594 (2002)], the generated single-photon pulses are 2 µs long. This duration exceeds the detector time resolution by three orders of magnitude and allows a close view into the structure of single-photon wave-packets. The talk will introduce the single-photon source used in this experiment and will show latest results.

Jakub Zielinski ``Entanglement of Cooled and Trapped Atoms''
      I present a scheme for testing nonclassical properties of atomic states. These states are antangled by the Velocity Selective Coherent Population Trapping (VSCPT) method. It is shown that it is possible to construct observables that can lead to correlation measurements that violate Bell\'s inequalities.

Mário Ziman ``Role of entanglement and correlations in dense coding''
      Superdense coding is known as an elementary example that shows the entanglement ``in action''. It is natural to ask whether this example cannot be used for a quantification of entanglement. We will generalize the original example to an arbitrary quantum state to obtain the capacity of noiseless quantum channel. Then we compare two communication strategies: on one side the ``dense coding scenario'' and on the other side the ``standard communication protocol''. It comes out that correlations are crucial in dense coding scenario. Several interesting remarks concerning the security will be discussed.

Stefano Zippilli ``Decoherence control in microwave cavities''
      We present a scheme able to protect the quantum states of a cavity mode against the decohering effects of photon loss. The scheme preserves quantum states with a definite parity, and improves previous proposals for decoherence control in cavities. It is implemented by sending single atoms, one by one, through the cavity. The atomic state gets first correlated to the photon number parity. The wrong parity results in an atom in the upper state. The atom in this state is then used to inject a photon in the mode via adiabatic transfer, correcting the field parity. By solving numerically the exact master equation of the system, we show that the protection of simple quantum states could be experimentally demonstrated using presently available experimental apparatus.

Zuzana Dzuráková
Ludmila Praxmeyer
Marián Rosko