ELEMENTS OF QUANTUM INFORMATION
CONTROLLED COLLISIONS MAGNETIC MICROTRAPS QUBIT STATES ON THE ATOM CHIP STATE-DEPENDENT MICROWAVE POTENTIALS QUBIT READOUT IN MICROTRAPS STABLE ?BER FABRY-PEROT CAVITIES FFP CAVITY FABRICATION AND PERFORMANCE ON-CHIP ATOM DETECTION WITH A FFP CAVITY SINGLE ATOM PREPARATION CONCLUSION REFERENCES TWO-DIMENSIONAL BOSE-EINSTEIN CONDENSATES IN A CO2-LASER OPTICAL LATTICE INTRODUCTION EXPERIMENTAL SETUP AND PROCEDURE EXPERIMENTAL RESULTS CONCLUSIONS CREATING AND PROBING LONG-RANGE ORDER IN ATOMIC CLOUDS COLLECTIVE COUPLING EXPERIMENTAL SETUP RING CAVITY DIPOLE TRAP FOR 85RB OPTICAL MOLASSES SIGNATURES OF COLLECTIVE ATOMIC RECOIL LASING BEAT NOTE OF FIELD MODES SPECTRA OF RECOIL-INDUCED RESONANCES ATOMIC TRANSPORT CREATING LONG-RANGE ORDER ANALYTIC TREATMENT FOR PERFECT BUNCHING RADIATION PRESSURE PHASE-LOCKING BY IMPERFECT MIRRORS SIMULATIONS OF ATOMIC TRAJECTORIES WITH FRICTION AND DIFFUSION LASING THRESHOLD SELF-SYNCHRONIZATION PROBING LONG-RANGE ORDER BRAGG SCATTERING HETERODYNED BRAGG SPECTRA MEASURING THE BRAGG SCATTERING PHASE DETECTING NEUTRAL ATOMS ON AN ATOM CHIP DETECTING SINGLE ATOMS MEASURING THE SCATTERED LIGHT: FLUORESCENCE DETECTION MEASURING THE DRIVING FIELD ABSORPTION ON RESONANCE REFRACTION CAVITIES MANY ATOMS IN A CAVITY CONCENTRIC CAVITY MINIATURIZATION PROPERTIES OF FIBER CAVITIES LOSS MECHANISMS FOR A CAVITY LOSSES DUE TO THE GAP LENGTH LOSSES DUE TO TRANSVERSAL MISALIGNMENT LOSSES DUE TO ANGULAR MISALIGNMENT FRESNEL RE?ECTIONS OTHER FIBER OPTICAL COMPONENTS FOR THE ATOM CHIP FLUORESCENCE AND ABSORPTION DETECTORS A SINGLE MODE TAPERED LENSED FIBER DIPOLE TRAP INTEGRATION OF FIBERS ON THE ATOM CHIP BUILDING FIBER CAVITIES THE SU-8 RESIST TEST OF THE SU-8 STRUCTURE PILOT TEST FOR ATOM DETECTION WITH SMALL WAISTS DROPPING ATOMS THROUGH A CONCENTRIC CAVITY DETECTING MAGNETICALLY GUIDED ATOMS X CONTENTS HIGH RESOLUTION RYDBERG SPECTROSCOPY OF ULTRACOLD RUBIDIUM ATOMS EXPERIMENTAL SETUP AND COLD ATOM PREPARATION VACUUM SYSTEM AND MAGNETO OPTICAL TRAP (MOT) RYDBERG LASER SYSTEM AND RYDBERG EXCITATION DETECTION OF THE RYDBERG ATOMS EXCITATION SEQUENCE SPECTROSCOPY OF RYDBERG STATES, |MJ| SPLITTING OF THE RYDBERG STATES SPATIAL AND STATE SELECTIVE ADDRESSING OF RYDBERG STATES SPATIAL SELECTIVE RYDBERG EXCITATION HYPER?NE SELECTIVE RYDBERG EXCITATION AUTLER-TOWNES SPLITTING CONCLUSION AND OUTLOOK PROSPECTS OF ULTRACOLD RYDBERG GASES FOR QUANTUM INFORMATION PROCESSING EXCITATION OF RYDBERG ATOMS FROM AN ULTRACOLD GAS VAN-DER-WAALS INTERACTION BLOCKADE OF EXCITATION IONIZATION STATES WITH PERMANENT ELECTRIC DIPOLE MOMENTS FÖRSTER RESONANCES QUANTUM STATE ENGINEERING WITH SPINS QUANTUM STATES OF SPINS DEUTSCH-JOSZA ALGORITHM THE DEUTSCH-JOSZA ALGORITHM IMPLEMENTATION OF THE 3-QUBIT DEUTSCH-JOSZA ALGORITHM USING LIQUID STATE NMR CONTENTS XI 11 2 2 1 2,3,4-TRI?UOROANILINE 11 2 2 2 PREPARATION OF PSEUDO-PURE STATES 11 2 2 3 RESULTS ON THE 3-QUBIT DJ-ALGORITHM SPIN QUANTUM COMPUTING IN THE SOLID STATE: S-BUS THE S-BUS CONCEPT SINGLE CRYSTAL CAF2 : CE3+ AS AN S-BUS SYSTEM EXPERIMENTAL DETAILS 3-QUBIT PSEUDO-PURE STATES 2-QUBIT DEUTSCH-JOSZA ALGORITHM 11 4 5 1 CONTROLLING NUCLEAR SPIN DECOHERENCE IN CAF2 : CE SUMMARY AND OUTLOOK IMPROVING THE PURITY OF ONE- AND TWO-QUBIT GATES QUANTUM GATE WITH BIT-?IP NOISE BLOCH-RED?ELD MASTER EQUATION PURITY DECAY NUMERICAL SOLUTION COHERENCE STABILIZATION FOR SINGLE QUBITS DYNAMICAL DECOUPLING BY HARMONIC DRIVING COHERENT DESTRUCTION OF TUNNELING COHERENCE STABILIZATION FOR A CNOT GATE HEISENBERG VS ISING COUPLING COHERENCE STABILIZATION BY AN AC FIELD IMPLEMENTATION WITH QUANTUM DOTS A APPENDIX HOW TO DISTILL ENTANGLEMENT FROM A FINITE AMOUNT OF QUBITS? ENTANGLEMENT DISTILLATION THE PROTOCOL CNOT DISTILLATION FOR A FINITE SET OF ENTANGLED SYSTEMS ITERATIVE DISTILLATION EXAMPLE OF THE ITERATIVE DISTILLATION FOR SMALL FINITE SETS EXPERIMENTAL QUANTUM SECRET SHARING THEORY THE GHZ-PROTOCOL THE |?? 4 ?-PROTOCOL THE SINGLE QUBIT PROTOCOL SECURITY OF THE PROTOCOLS EXPERIMENT THE SINGLE-QUBIT PROTOCOL FREE SPACE QUANTUM KEY DISTRIBUTION: TOWARDS A REAL LIFE APPLICATION SETUP TRANSMITTER UNIT FREE SPACE LINK RECEIVER UNIT SYNCHRONISATION AND AUTOMATIC ALIGNMENT CONTROL SIFTING, ERROR CORRECTION AND PRIVACY AMPLI?CATION CONTINUOUS VARIABLE ENTANGLEMENT BETWEEN FREQUENCY MODES SIDEBAND SEPARATION PICTORIAL DESCRIPTION EXPERIMENT AND RESULTS CONCLUSION AND DISCUSSION FACTORIZATION OF NUMBERS WITH PHYSICAL SYSTEMS CHIRPING A TWO-PHOTON TRANSITION CHIRPED LASER PULSES EXCITATION PROBABILITY AMPLITUDE EXAMPLE FOR FACTORIZATION DRIVING A ONE-PHOTON TRANSITION MODEL FLOQUET LADDER PULSE TRAIN FACTORIZATION FACTORIZATION WITH FLOQUET LADDER FACTORIZATION WITH A PULSE TRAIN NMR-EXPERIMENT QUANTUM ALGORITHMS FOR NUMBER FIELDS OUTLINE OF THE SURVEY WHY NUMBER FIELDS? SOME HISTORY OF THE SUBJECT GEOMETRY OF NUMBERS NUMBER FIELDS LATTICES INTEGRAL ELEMENTS THE CLASS NUMBER THE REGULATOR COMPLEXITY RESULTS REDUCTION REDUCED IDEALS INFRASTRUCTURE GEOMETRIC INTERPRETATION OF G RESULTS FROM ANALYTIC NUMBER THEORY DISTRIBUTION OF PRIME NUMBERS CLASS NUMBER FORMULAS EXAMPLES OF MINIMA DISTRIBUTIONS COMPUTING THE REGULATOR REAL QUADRATIC CASE HALLGREN’S ALGORITHM GENERALIZATION OF THE WEAK PERIODICITY CONDITION COMPUTATION OF OTHER INVARIANTS THE PRINCIPAL IDEAL PROBLEM COMPUTING THE CLASS NUMBER IMPLEMENTATION COMPLEXITY OF PHYSICAL PROCESSES AS A NATURAL EXTENSION OF COMPUTATIONAL COMPLEXITY SIMILAR COMPLEXITY BOUNDS FOR DIFFERENT TASKS RELATING CONTROL PROBLEMS TO HARD COMPUTATIONAL PROBLEMS THE NEED FOR A CONTROL-THEORETIC FOUNDATION OF COMPLEXITY HAMILTONIANS THAT COMPUTE AUTONOMOUSLY IMPLEMENTATION OF GENERALIZED MEASUREMENTS WITH MINIMAL DISTURBANCE ON A QUANTUM COMPUTER MINIMAL-DISTURBING IMPLEMENTATIONS OF POVMS GENERALIZED MEASUREMENTS OF QUANTUM SYSTEMS POSITIVE-OPERATOR VALUED MEASURES ORTHOGONAL MEASUREMENTS DISTURBANCE OF A GENERALIZED MEASUREMENT MINIMAL-DISTURBING IMPLEMENTATION OF A POVM SYMMETRIC MATRICES AND THEIR STRUCTURE REPRESENTATIONS OF FINITE GROUPS PROJECTIVE REPRESENTATIONS SYMMETRY OF A MATRIX AND SCHUR’S LEMMA SYMMETRIC POVMS DE?NE MATRICES WITH SYMMETRY IMPLEMENTATION OF SYMMETRIC POVMS CYCLIC AND HEISENBERG-WEYL GROUPS CYCLIC GROUPS HEISENBERG-WEYL GROUPS CONCLUSIONS AND OUTLOOK CONTENTS XV FULL COUNTING STATISTICS OF INTERACTING ELECTRONS CONCEPTS OF FCS FULL COUNTING STATISTICS IN INTERACTING QUANTUM DOTS FCS OF A SET FOR INTERMEDIATE STRENGTH CONDUCTANCE NON-MARKOVIAN EFFECTS: RENORMALIZATION AND FINITE LIFETIME BROADENING OF CHARGE STATES KELDYSH ACTION AND CGF IN MAJORANA REPRESENTATION FCS AND COULOMB INTERACTION IN DIFFUSIVE CONDUCTORS MODEL AND EFFECTIVE ACTION “COLD ELECTRON” REGIME “HOT ELECTRON” REGIME SUMMARY QUANTUM LIMIT OF THE CARNOT ENGINE SPIN-OSCILLATOR MODEL BASIC DE?NITIONS THERMODYNAMIC VARIABLES FOR G MASTER EQUATION LINDBLAD SUPEROPERATOR TIME SLOT OPERATORS MACHINE CYCLES CHOICE OF AMPLITUDES A(J) ± AND CONTROL FUNCTIONS ?(J)(?) HEAT AND WORK ENERGY BALANCE FLUCTUATIONS NUMERICAL RESULTS HEAT ENGINE HEAT PUMP LONGTIME LIMIT QUANTUM LIMIT AND CLASSICAL LIMIT SUMMARY AND CONCLUSIONS