TITLE AND ABSTRACTS

K.AUDENAERT

Applications of Convex Analysis in QIT

C.BENNETT

H.BRIEGEL

Entanglement purification of cluster states and other multi-partite entangled states

Cluster states have been shown to be the central resource in the one-way quantum computer. In this talk we show how cluster states, in a multi-party scenario, can be purifed by a multi-party purification protocol, which is remarkably robust against local noise.  The protocol can be generalized to a class of graph states, including e.g. the GHZ states and a variety of quantum error correcting codes. As a consequence, the class of states that are purified is useful for both (distributed) quantum computation and for multi-party communication.

S.BOSE

Schemes to Probe Quantum Mechanical Behaviour of MacroscopicObjects

I will describe a general scheme through which the coherence between microscopically distinct states of a macroscopic object can be probed. The system consists of a qubit coupled to a harmonic oscillator measuring apparatus. Parameter domains for some potentially feasible implementations will be described. As a second part of the talk, I will describe a duality in entanglement of identical objects, and how it might help to explore the loss of the ability of identical objects to behave indistinguishably as they are made more macroscopic.

R.CLEVE

Exponential algorithmic speedup by a quantum walk

We construct a black box problem that can be solved exponentially faster on a quantum computer than on a classical computer. The quantum algorithm is based on a continuous time quantum walk, and thus employs a different technique from previous quantum algorithms based on quantum Fourier transforms. We show how to implement the quantum walk efficiently in our black box setting. We then show how this quantum walk can be used to solve our problem by rapidly traversing a graph. Finally, we prove that no classical algorithm can solve this problem  with high probability in subexponential time.

C.CREPEAU

A length n QECC probabilistically correcting (n-1)/2 arbitrary errors

It is an immediate result of the no cloning theorem that no Quantum Error Correcting Code (QECC) of length n can fix n/2 erasure errors because that would imply that from two disjoint parts of a codeword of size smaller or equal to n/2, two copies of the codeword could be reconstructed. This statement is valid regardless of the dimension of the coding Hilbert space. Another well known result of QECCs is that a length n code can fix t arbitrary single position errors if and only if it can fix 2t erasure errors. This implies that no QECC of length n can fix more than n/4 arbitrary errors, regardless of the dimension of the coding Hilbert space. In this paper, we show the existence of QECCs of length n that can fix (n-1)/2 arbitrary single position errors except with n exponentially small error probability

M. D’ARIANO

Characterization and Engineering of Quantum Operations

When a quantum system enters a quantum device/apparatus, its state transforms according to a linear, trace-non-increasing, and completely positive map, the so-called ``Quantum Operation'' (QO), which describes the general conditioned dynamics through the device. In this talk we address the problem of how to achieve a complete characterization of a QO, and how to discriminate among a set of different QO's . We will see that there are special non-classical states that, when used as input for the QO, carry a complete information about it. Methods especially suited to measuring apparatuses are presented, and, as an application, a scheme for an experimental absolute characterization of a photo-detector is proposed. Connections with the problem of designing programmable QO devices are given in the concluding part.

Quantum Coherence in a Single Cooper pair box read out by a Single Electron Transistor

We have fabricated several Single Cooper pair Boxes (SCBs) and measured their characteristics using a Radio-Frequency Single-Electron-Transistor (RF-SET). In the normal state we find an e-periodic staircase, and in the superconducting case we find a 2e periodic staircase. Some samples show a shorter step at the gate voltages corresponding to odd numbers of electrons. By irradiating the SCB with microwaves, we can populate the higher level so that peaks develop in the staircase pattern. By plotting frequency as a function of the location of these peaks, we can map out the energy levels for different values of magnetic field. We can also extract the charging energy E_C and the Josephson coupling energy E_J. By applying short dc-pulses to the gate of our SCB, with a varying pulse length, we observe how the probability of finding the system in the exited state oscillates as a function of the pulse duration.

R. DE WOLF

Quantum Private Information Retrieval

Private information retrieval concerns the following problem: a user wants to retrieve the i-th bit from an n-bit database that is replicated over k servers, but he wants to do that privately: none of the servers should learn any information about i. We are interested in the amount of communication needed for this, comparing classical and quantum PIR schemes.  For 1 server this amount is linear in n, classically as well as quantumly (Nayak). For 2 servers, the best known classical PIR scheme uses n^{1/3} communication.  We exhibit a quantum 2-server PIR scheme that uses n^{3/10} qubits of communication.  Our main tool is a certain reduction from 2 classical servers to 1 quantum server.
We get similar quantum improvements for more than 2 servers. We also prove a new lower bound for 2-server PIR schemes in which the servers send only short answers.

Contextual Realization of the "Universal Optimal Cloning and U-NOT  Machines" by Optical Parametric Amplification.

A contextual experimental demonstration of the UOQCM and of the U-NOT gate for quantum information is reported. The adopted apparatus, a Quantum Injected Optical Parametric Amplifier (QIOPA), realizes simultaneously and contextually two processes which are "forbidded" by fundamental quantum limitations, namely violate the content of two distinct axioms of structural quantum theory, namely, the "linerarity" and the "complete positivity" of any quantum map. The subtle link between these concepts, suggested by the present contextual experiment are discussed.

J. ESCHNER

Experiments with single trapped ions: From quantum optics to quantum information processing

Experiments with single trapped and laser-cooled ions have provided major contributions to the field of quantum optics with atoms and photons. Trapped ions are localised much below an optical wavelength, they provide atomic transitions with long coherence times, offer a very high degree of isolation from the environment, and they allow full control over the motional state by laser cooling, and state detection with near-unity efficiency. The same properties make single ions very promising candidates to implement schemes for quantum information processing. I will summarize the relevant techniques and present recent experimental progress towards quantum information processing with trapped 40Ca+ ions. In particular, the Deutsch-Jozsa quantum algorithm has been implemented with two qubits in a single Ca ion, and the Cirac-Zoller quantum CNOT gate between two ions has been realised. The coherent coupling of a single ion to an optical cavity will also be presented.

R.FAZIO

I will discuss the entanglement near a quantum phase transition by analyzing the properties of the concurrence for a class of exactly solvable models in one dimension. Entanglement can be classified in the framework of the scaling theory of phase transition. There is a profound differences between the classical correlations, whose correlation lenght diverges at the phase transition, and non-local quantum correlations that remain, in general, short ranged. In the last part of the presentation I will report on some results on the dynamics of entangled in spin chains.

E.HINDS

I describe experiments in which Bose-Einstein condensates and cold atom clouds are held by a microscopic magnetic trap near a room temperature surface. Relaxation processes associated with the atom surface coupling are studied.  I consider the possibilities for using atom chips as a basis for quantum information processing

M.HORODECKI

Entanglement and correlations in quantum compound systems. 

R.JOZSA

Entanglement cost of generalised measurements

Bipartite entanglement is one of the fundamental quantifiable resources of quantum information theory. We propose a new application of this resource to the theory of quantum measurements. According to Naimark's theorem any rank 1 generalised measurement (POVM) may be represented as a von Neumann measurement in an extended (tensor product) space of the system plus an ancilla. By considering a suitable average of the entanglements of these measurement directions, and minimising over all Naimark extensions, we define a notion of entanglement cost of the POVM. We describe some surprising basic properties of this quantity

D.LOSS

M.MOSCA

On the quantum derandomization of algorithms

We develop techniques for taking a certain class of algorithms that succeed with high probability and turning them into algorithms that succeed with certainty (i.e. with probability 1).  We show how to compute the Quantum Fourier Transform exactly for any order (joint work with Zalka). This allows us to solve the open problem of exactly computing discrete logarithms in groups of a known size.We also define a reasonable model of exact computation in which we can derandomize Shor's factorization algorithm.

R.MUNOZ-TAPIA

Optimal estimation of information using quantum states

There are certain types of information that can not be discretized. Imagine that Alice wants to indicate a direction in space to Bob. If  Alice and Bob are allowed to use quantum systems for this communication process, the natural question that arises is: what are the best system Alice can use to codify this information and what is the best measuring strategy Bob can perform. This problem has  some interesting mathematical connexions with orthogonal polynomials and  discretizations of a continuous group. I will discuss different optimal strategies and under different restricttions. I will pay  some attention  to optimal strategies when only local measurements are allowed, probably the most important case from the practical point of view. Finally,  I will review some recent progress in  aligning reference frames using quantum systems.

M.NIELSEN

Majorization and complexity lower bounds for quantum dynamics

How much time is required to implement a unitary operation, given a particular Hamiltonian, and fast local unitary operations?  In this talk I   explain how the theory of majorization can be used to prove some general  lower bounds on this time, and can be used to derive exact answers in  some specific instances.

J.PARRONDO

We will present a review of the so-called Parrondo's paradox, with special attention to the most recent results on collective effects in this type of gambling games. Finally, we will briefly discuss some extensions of the paradox to quantum systems.

A.SANPERA

Multipartite entanglement detection using entanglement witnesses

Entanglement witnesses do not only provide a mathematical criterium to test if a given state is entangled or not but also they can easily be implemented experimentally by means of few local measurements. This method allows to detect genuine 3 and 4 partite entanglement. We will discuss also some of our results concerning the relation between Bell inequalities and entanglement witnesses

B.SCHUMACHER

What is information?

Quantum information theory forces us to reconsider just what we mean by the term "information".  Is there a more general physical view of information that encompasses both quantum and classical concepts? This talk will try to present such a view.  An information theory is a theory of the reversibility (or approximate reversibility) of state changes under a restricted set of feasible operations. Within a given physical theory (e.g., quantum mechanics), there may be several distinct well-motivated choices for the feasible set, depending on the physical situation.  Thus, there can be several distinct, inequivalent ideas of "information".  We will illustrate this approach by exploring a specific type of quantum information, shedding new light on old results and suggesting new problems that have not yet been solved.

E.SHAPIRO

DNA molecule provides a computing machine with both data and fuel The unique properties of DNA make it a fundamental building block in the fields of supramolecular chemistry, nanotechnology, nano-circuits, molecular switches, molecular devices and molecular computing. In our recently introduced autonomous molecular automaton, DNA molecules serve as input, output and software while the hardware consists of DNA restriction and ligation enzymes using ATP as fuel. In addition to information, DNA also stores energy, available upon hybridization of complementary strands or hydrolysis of its phosphodiester backbone. Here we show that a single DNA molecule can provide both the input data and all the necessary fuel for a molecular automaton. Each computational step of the automaton consists of a reversible software molecule/input molecule hybridization followed by an irreversible software-directed cleavage of the input molecule, which drives the computation forward by increasing entropy and releasing heat. The cleavage utilizes a hitherto unknown capability of the restriction enzyme FokI, which serves as the hardware, to operate on a non-covalent software/input hybrid. In the previous automaton, software/input ligation consumed one software molecule and two ATP molecules per step. As ligation is not performed in this automaton, a fixed amount of software and hardware molecules can, in principle, process any input molecule of any length without external energy supply. Our experiments demonstrate 3x10^12 automata per  microliter performing 6.6x10^10 transitions per s per microliter with transition fidelity of 99.9%, dissipating about 5x10^-9 W/microliter as heat at ambient temperature.

U.VAZIRANI

R.WERNER

Shared Entanglement Fidelity

It is well-known that three parties cannot be mutually maximallyentangled, as this would allow breaking the no-cloning theorem by teleportation. In this talk we study quantitative bounds on the pairwise entanglement, when entanglement is measured by the maximal fidelity with respect to a maximally entangled reference state. For three parties we study in detail the states with maximal local entanglement, and their dependence on Hilbert space dimension and the choice of reference states. It turns out that the highest local entanglement is possible when the holonomy implied by the choice of reference states is trivial, i.e., all reference states can be simultaneously brought into Schmidt form. We also maximize the total fidelity between a central node and many other partners, resulting in an optimal telecloner, and the maximal mean pair fidelity for a complete graph. The limit of many particles in the last two problems can be analyzed using mean field quantum statistical mechanics.

C.WUNDERLICH

Electrodynamically trapped Yb+ ions and ion "molecules" for quantuminformation processing

 Recent experimental results relevant for quantum information processing  obtained with electrodynamically trapped Yb+ ions are reported. This includes the realization of a variety of quantum channels and the self-learning estimation of arbitrary qubit states. In addition, novel ideas for coherent manipulation of internal and external degrees of freedom of trapped ions will be outlined. In a suitably modified trap a string of ions can be treated like a molecule used for spin resonance experiments:  The collection of trapped ions can be viewed as a N-qubit molecule with adjustable spin-spin coupling. 

H.ZBINDEN

How to Extend the Range of Quantum Key Distribution

Faint laser QKD has been demonstrated over several tenths of km of optical fibres and is currently on the verge of commercialisation. However, its range is limited. In presence of high transmission losses, the eavesdropper can efficiently take profit of the Poisson distribution of the number of photons in the pulses. Hence, if unconditional security is demanded, low average photon number and thorough privacy amplification must be applied. This reduces the number of transmitted secure bit's almost to zero after about 50 km. We present a novel protocol, which extends the range of unconditional secure QKD to some 100 km. This is almost what you can achieve using perfect single photon sources. If you want to go further, you either need a secure intermediate station, a quantum repeater (with a quantum memory) or a quantum relay