FUNDAMENTALS OF QUANTUM OPTICS AND QUANTUM INFORMATION

By D. DANIU

CONTENTS PART I QUANTUM OPTICS QUANTUM MECHANICAL BACKGROUND THE MATHEMATICAL FRAMEWORK COMPLEX VECTOR SPACES BASES AND VECTOR DECOMPOSITION LINEAR OPERATORS MATRIX REPRESENTATION OF OPERATORS DESCRIPTION OF QUANTUM SYSTEMS PHYSICAL OBSERVABLES QUANTUM MECHANICAL HAMILTONIAN ALGEBRAIC APPROACH FOR THE HARMONIC OSCILLATOR OPERATORS AND MEASUREMENT HEISENBERG UNCERTAINTY PRINCIPLE TIME EVOLUTION: THE SCHR¨ODINGER EQUATION HEISENBERG PICTURE DENSITY OPERATOR PURE AND MIXED STATES EXPECTATION VALUE OF AN OPERATOR REDUCED DENSITY OPERATOR TIME EVOLUTION: THE VON NEUMANN EQUATION PROBLEMS QUANTUM THEORY OF RADIATION MAXWELL’S EQUATIONS AND FIELD QUANTIZATION FIELD QUANTIZATION IN OPEN SPACE FIELD QUANTIZATION IN A CAVITY QUANTUM STATES OF THE FIELD SINGLE-MODE CAVITY FIELD FREE ELECTROMAGNETIC FIELD PHOTON DETECTION AND CORRELATION FUNCTIONS REPRESENTATIONS OF THE FIELD COHERENT STATE REPRESENTATION QUASI-PROBABILITY DISTRIBUTIONS ATOM IN AN EXTERNAL RADIATION FIELD ONE ELECTRON ATOM ELECTRONIC STATES OF AN ATOM ANGULAR MOMENTUM AND SPIN IN QUANTUM THEORY SPIN–ORBIT COUPLING COUPLING OF RADIATION FIELD WITH ATOMIC ELECTRON TWO-LEVEL ATOM INTERACTING WITH MONOCHROMATIC FIELDS INTERACTION OF AN ATOM WITH A CLASSICAL FIELD INTERACTION OF AN ATOM WITH A QUANTIZED FIELD: JAYNES–CUMMINGS MODEL TWO-LEVEL ATOM IN A HARMONIC POTENTIAL QUANTUM SYSTEM COUPLED TO A RESERVOIR SINGLE STATE COUPLED TO A CONTINUUM OF STATES SPONTANEOUS DECAY OF AN EXCITED ATOM IN OPEN SPACE THREE-LEVEL ATOM SYSTEM-RESERVOIR INTERACTION GENERAL MASTER EQUATION SPONTANEOUS DECAY OF A TWO-LEVEL ATOM DRIVEN TWO-LEVEL ATOM QUANTUM STOCHASTIC WAVEFUNCTIONS GENERAL FORMULATION APPLICATION TO A DRIVEN TWO-LEVEL ATOM HEISENBERG–LANGEVIN EQUATIONS OF MOTION APPLICATION TO A TWO-LEVEL ATOM CAVITY QUANTUM ELECTRODYNAMICS SINGLE MODE CAVITY FIELD COUPLED TO A RESERVOIR MASTER EQUATION STOCHASTIC WAVEFUNCTIONS FOKKER–PLANCK EQUATION ATOM IN A DAMPED CAVITY SINGLE PHOTONS ON DEMAND FROM ATOM IN A CAVITY FIELD PROPAGATION IN ATOMIC MEDIA PROPAGATION EQUATION FOR SLOWLY VARYING ELECTRIC FIELD FIELD PROPAGATION IN A TWO-LEVEL ATOMIC MEDIUM FIELD PROPAGATION IN A THREE-LEVEL ATOMIC MEDIUM PART II QUANTUM INFORMATION ELEMENTS OF CLASSICAL COMPUTATION BITS AND MEMORY CIRCUITS WIRES AND GATES CIRCUIT EXAMPLES ELEMENTS OF UNIVERSAL CIRCUIT CONSTRUCTION COMPUTATIONAL RESOURCES REVERSIBLE COMPUTATION FUNDAMENTALS OF QUANTUM INFORMATION QUANTUM BITS AND MEMORY QUANTUM CIRCUITS ONE QUBIT GATES TWO AND MORE QUBIT GATES QUBIT MEASUREMENT NO-CLONING THEOREM GENUINE PHYSICAL QUBITS SPIN 2 QUBIT PHOTON POLARIZATION QUBIT ENTANGLEMENT, DECOHERENCE AND QUANTUM ERASURE QUANTUM TELEPORTATION AND DENSE CODING QUANTUM CRYPTOGRAPHY BB84 PROTOCOL B92 PROTOCOL EPR PROTOCOL EINSTEIN–PODOLSKY–ROSEN PARADOX LOCAL HIDDEN VARIABLE AND BELL’S INEQUALITY VIOLATIONS OF BELL’S INEQUALITY GREENBERGER–HORNE–ZEILINGER EQUALITY ENTROPY AND INFORMATION THEORY PRINCIPLES OF QUANTUM COMPUTATION OPERATION OF QUANTUM COMPUTER UNIVERSAL GATES FOR QUANTUM COMPUTATION BUILDING BLOCKS OF A QUANTUM COMPUTER QUANTUM ALGORITHMS DEUTSCH ALGORITHM DEUTSCH–JOZSA ALGORITHM GROVER ALGORITHM QUANTUM FOURIER TRANSFORM QUANTUM COMPUTER SIMULATING QUANTUM MECHANICS ERROR CORRECTION AND FAULT–TOLERANT COMPUTATION CLASSICAL ERROR CORRECTION QUANTUM ERROR CORRECTION FAULT–TOLERANT QUANTUM COMPUTATION PHYSICAL IMPLEMENTATIONS OF QUANTUM COMPUTATION 10 1 REQUIREMENTS FOR PHYSICAL IMPLEMENTATIONS OF QUANTUM INFORMATION PROCESSING 10 2 RYDBERG ATOMS IN MICROWAVE CAVITY 10 2 1 LOGIC GATES AND MULTIPARTICLE ENTANGLEMENT 10 2 2 SCHR¨ODINGER CAT STATES OF THE CAVITY FIELD 10 3 ION-TRAP QUANTUM COMPUTER 10 4 CAVITY QED-BASED QUANTUM COMPUTER 10 5 OPTICAL QUANTUM COMPUTER 10 6 QUANTUM DOT ARRAY QUANTUM COMPUTER 10 7 OVERVIEW AND CLOSING REMARKS FURTHER READING