Elements Of Quantum Information

Elements of Quantum Information' introduces the reader to the fascinating field of quantum information processing, which lives on the interface between computer science, physics, mathematics, and engineering. This interdisciplinary branch of science thrives on the use of quantum mechanics as a resource for high potential modern applications. With its wide coverage of experiments, applications, and specialized topics - all written by renowned experts - 'Elements of Quantum Information' provides an indispensable up-to-date account of the state of the art of this rapidly advancing field and takes the reader straight up to the frontiers of current research. The articles have first appeared as a special issue of the journal 'Fortschritte der Physik/Progress of Physics'. Since then, they have been carefully updated. The book will be an inspiring source of information and insight for anyone researching and specializing in experiments and theory of quantum information.

Wolfgang P. Schleich, born in 1957, is head of the Institute of Quantum Physics at the University of Ulm, Germany, and Adjunct Professor at the University of North Texas in Denton, USA. While working at the Universities of New Mexico, Albuquerque, of Texas at Austin and the Max Planck Institute for Quantum Physics, Garching, Germany, he has collaborated with world leaders in physics such as M.O. Scully, J.A. Wheeler and H. Walther. Professor Schleich has published more than 230 papers on problems of quantum optics, foundations of quantum mechanics and general relativity and is the author of the highly acclaimed textbook Quantum Optics in Phase Space. For his work he has received numerous awards and honors, including the Ernst Abbe Medal of the International Commission for Optics, the Gottfried Wilhelm Leibniz Prize of the German Science Foundation and the Max Planck Award. He is a Fellow of the Institute of Physics, the American Physical Society and the Optical Society of America and has been elected a member of several academies, such as the Leopoldina, the Heidelberg Academy of Science, and the Royal Danish Academy of Sciences and Letters.
Herbert Walther (1935-2006) received his Ph.D. from the University of Heidelberg in 1962. After working at various universities in Germany, France and the United States, Professor Walther accepted a post as Professor of Physics at the University of Munich in 1975, from which he took retirement in 2003. From 1981, Professor Walther also worked for the Max Planck Society. He founded the Max Planck Institute of Quantum Optics in Garching, and headed the Institute as its Director until his retirement. From 1990 to 1996, he acted as the Max Planck Society's Vice President. Professor Walther was a Fellow and member of many professional physics organizations and scientific boards. He was awarded numerous honours and awards, among them the Max Born Prize (1978) and the Humboldt Medal (1998).

Preface to the Book.
Preface to the Journal.
List of Contributors.
1 The Deterministic Generation of Photons by Cavity Quantum Electrodynamics (H. Walther).
1.1 Introduction.
1.2 Oscillatory Exchange of Photons Between an Atom and a Cavity Field.
1.3 Other Microwave Cavity Experiments.
1.4 Cavity QED Experiments in the Visible Spectral Region.
1.5 Conclusions and Outlook.
References.
2 Optimization of Segmented Linear Paul Traps and Transport of Stored Particles (Stephan Schulz, Ulrich Poschinger, Kilian Singer, and Ferdinand Schmidt-Kaler).
2.1 Introduction.
2.2 Optimization of a Two-layer Microstructured Ion Trap.
2.3 Open Loop Control of Ion Transport.
2.4 Outlook.
A Appendix.
References.
3 Transport Dynamics of Single Ions in Segmented Microstructured Paul Trap Arrays (R. Reichle, D. Leibfried, R. B. Blakestad, J. Britton, J.D. Jost, E. Knill, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland).
3.1 Introduction.
3.2 Classical Equations of Motion.
3.3 Classical Dynamics of Ion Transport.
3.4 Quantum and Classical, Dragged Harmonic Oscillators with Constant Frequency.
3.5 The Dragged Quantum Harmonic Oscillator.
3.6 Transport Dynamics in aWell-controlled Regime.
3.7 Please supply a short title.
3.8 Conclusions.
A Appendix.
References.
4 Ensemble Quantum Computation and Algorithmic Cooling in Optical Lattices (M. Popp, K. G.H. Vollbrecht, and J. I. Cirac).
4.1 Introduction.
4.2 Physical System.
4.3 Ensemble Quantum Computation.
4.4 Cooling with Filtering.
4.5 Algorithmic Ground State Cooling.
4.6 Conclusion.
References.
5 Quantum Information Processing in Optical Lattices and Magnetic Microtraps (Philipp Treutlein, Tilo Steinmetz, Yves Colombe, Benjamin Lev, Peter Hommelhoff, Jakob Reichel, Markus Greiner, Olaf Mandel, Artur Widera, Tim Rom, Immanuel Bloch, and Theodor W. Hänsch).
5.1 Introduction.
5.2 Optical Lattices.
5.3 Magnetic Microtraps.
5.4 Conclusion.
References.
6 Two-dimensional Bose-Einstein Condensates in a CO2-laser Optical Lattice (Giovanni Cennini, Carsten Geckeler, Gunnar Ritt, Tobias Salger, and Martin Weitz).
6.1 Introduction.
6.2 Experimental Setup and Procedure.
6.3 Experimental Results.
6.4 Conclusions.
References.
7 Creating and Probing Long-range Order in Atomic Clouds (C. von Cube, S. Slama, M. Kohler, C. Zimmermann, and Ph.W. Courteille).
7.1 Introduction.
7.2 Collective Coupling.
7.3 Creating Long-range Order.
7.4 Probing Long-range Order.
7.5 Conclusion.
References.
8 Detecting Neutral Atoms on an Atom Chip (Marco Wilzbach, Albrecht Haase, Michael Schwarz, Dennis Heine, Kai Wicker, Xiyuan Liu, Karl-Heinz Brenner, Sönke Groth, Thomas Fernholz, Björn Hessmo, and Jörg Schmiedmayer).
8.1 Introduction.
8.2 Detecting Single Atoms.
8.3 Properties of Fiber Cavities.
8.4 Other Fiber Optical Components for the Atom Chip.
8.5 Integration of Fibers on the Atom Chip.
8.6 Pilot Test for Atom Detection with Small Waists.
8.7 Conclusion.
References.
9 High Resolution Rydberg Spectroscopy of Ultracold Rubidium Atoms (Axel Grabowski, Rolf Heidemann, Robert Löw, Jürgen Stuhler, and Tilman Pfau).
9.1 Introduction.
9.2 Experimental Setup and Cold Atom Preparation.
9.3 Spectroscopy of Rydberg States, |m_j| Splitting of the Rydberg States.
9.4 Spatial and State Selective Addressing of Rydberg States.
9.5 Autler-Townes Splitting.
9.6 Conclusion and Outlook.
References.
10 Prospects of Ultracold Rydberg Gases for Quantum Information Processing (Markus Reetz-Lamour, Thomas Amthor, Johannes Deiglmayr, Sebastian Westermann, Kilian Singer, André Luiz de Oliveira, Luis Gustavo Marcassa, and Matthias Weidemüller).
10.1 Introduction.
10.2 Excitation of Rydberg Atoms from an Ultracold Gas.
10.3 Van-der-Waals Interaction.
10.4 States with Permanent Electric Dipole Moments.
10.5 Förster Resonances.
10.6 Conclusion.
References.
11 Quantum State Engineering with Spins (Andreas Heidebrecht, Jens Mende, and Michael Mehring).
11.1 Introduction.
11.2 Deutsch-Josza Algorithm.
11.3 Entanglement of an Electron and Nuclear Spin in ¹⁵N@C₆₀.
11.4 Spin Quantum Computing in the Solid State: S-bus.
11.5 Summary and Outlook.
References.
12 Improving the Purity of One- and Two-qubit Gates (Sigmund Kohler and Peter Hänggi).
12.1 Introduction.
12.2 Quantum Gate with Bit-flip Noise.
12.3 Coherence Stabilization for Single Qubits.
12.4 Coherence Stabilization for a CNOT Gate.
12.5 Conclusions.
A Appendix.
References.
13 How to Distill Entanglement from a Finite Amount of Qubits? (Stefan Probst-Schendzielorz, Thorsten Bschorr, and Matthias Freyberger).
13.1 Introduction.
13.2 Entanglement Distillation.
13.3 CNOT Distillation for a Finite Set of Entangled Systems.
13.4 Example of the Iterative Distillation for Small Finite Sets.
13.5 Conclusions.
A Appendix.
References.
14 Experimental Quantum Secret Sharing (Christian Schmid, Pavel Trojek, Sascha Gaertner, Mohamed Bourennane, Christian Kurtsiefer, Marek Zukowski, and Harald Weinfurter).
14.1 Introduction.
14.2 Theory.
14.3 Experiment.
14.4 Conclusion.
References.
15 Free Space Quantum Key Distribution: Towards a Real Life Application (Henning Weier, Tobias Schmitt-Manderbach, Nadja Regner, Christian Kurtsiefer, and Harald Weinfurter).
15.1 Introduction.
15.2 Setup.
15.3 Conclusion.
References.
16 Continuous Variable Entanglement Between Frequency Modes (Oliver Glöckl, Ulrik L. Andersen, and Gerd Leuchs).
16.1 Introduction.
16.2 Sideband Separation.
16.3 Experiment and Results.
16.4 Conclusion and Discussion.
References.
17 Factorization of Numbers with Physical Systems (Wolfgang Merkel, Ilya Sh. Averbukh, Bertrand Girard, Michael Mehring, Gerhard G. Paulus, and Wolfgang P. Schleich).
17.1 Introduction.
17.2 Chirping a Two-photon Transition.
17.3 Driving a One-photon Transition.
17.4 Factorization.
17.5 NMR-experiment.
17.6 Conclusions.
References.
18 Quantum Algorithms for Number Fields (Daniel Haase and Helmut Maier).
18.1 Introduction.
18.2 Geometry of Numbers.
18.3 Reduction.
18.4 Results from Analytic Number Theory.
18.5 Examples of Minima Distributions.
18.6 Computing the Regulator.
18.7 Computation of Other Invariants.
References.
19 Implementation Complexity of Physical Processes as a Natural Extension of Computational Complexity (Dominik Janzing).
19.1 Introduction.
19.2 Similar Complexity Bounds for Different Tasks.
19.3 Relating Control Problems to Hard Computational Problems.
19.4 The Need for a Control-theoretic Foundation of Complexity.
19.5 Hamiltonians that Compute Autonomously.
References.
20 Implementation of Generalized Measurements with Minimal Disturbance on a Quantum Computer (Thomas Decker and Markus Grassl).
20.1 Introduction.
20.2 Minimal-disturbing Implementations of POVMs.
20.3 Symmetric Matrices and their Structure.
20.4 Implementation of Symmetric POVMs.
20.5 Cyclic and Heisenberg-Weyl Groups.
20.6 Conclusions and Outlook.
References.
21 Full Counting Statistics of Interacting Electrons (D. A. Bagrets, Y. Utsumi, D. S. Golubev, and Gerd Schön).
21.1 Introduction.
21.2 Concepts of FCS.
21.3 Full Counting Statistics in Interacting Quantum Dots.
21.4 FCS and Coulomb Interaction in Diffusive Conductors.
21.5 Summary.
References.
22 Quantum Limit of the Carnot Engine (Friedemann Tonner and Günter Mahler).
22.1 Introduction.
22.2 Spin-oscillator Model.
22.3 Master Equation.
22.4 Machine Cycles.
22.5 Numerical Results.
22.6 Summary and Conclusions.
References.
Appendix: Colour Plates.
Index.