Quantum Optics and Quantum Information. Edition No. 1

Table of Contents

1. Introduction
1.1 From wave-functions to Dirac notation
1.2 Time evolution and unitary mappings
2. Two state systems and qubits
2.1 Pauli spin matrices
2.2 The Bloch sphere
2.3 Two qubit systems
2.4 The no cloning theorem
3. The density operator and density matrix
3.1 Quantum ensembles & the density operator
3.2 Purity of quantum states
3.3 The Bloch sphere and the density matrix
3.4 The reduced density operator
3.5 Correlation and entanglement
3.6 Distance between two states
4. Photons and quantum field states
4.1 Quantised cavity field, free field, and the harmonic oscillator.
4.2 Cavity vs. running wave quantization
4.3 Polarisation of photons
4.4 The number state
4.5 The thermal field
4.6 The coherent state
5. Atom and photon
5.1 Atoms and cavities
5.1.1 The Jaynes-Cummings cavity-atom model
5.1.2 A cavity system with a three-level atom: photons on demand
5.1.3 The Dicke model
5.2 Atoms and non-linear optical processes
5.2.1 Parametric down-conversion
5.2.2 Two-mode Squeezing
5.2.3 Single mode Squeezing
6. Quasi-probabilities, operators, and operator algebra
6.1 Operator theorems (I-IV)
6.2 Displacement operator
6.3 Coherent state as a basis
6.4 P-function & Q-function
6.5 Wigner function
6.6 The quantum phase operator
7. Detector theory and correlation functions
7.1 Detectors
7.2 Theory of a physical detector
7.3 The photon number distribution and photon counting
7.4 Correlation functions: G1, g1, and Young's slits
7.5 Correlation functions: g2 and the Hanbury-Brown-Twiss experiment
8. The Beam-splitter
8.1 Beam-splitter theory
8.2 The beam-splitter and phase choices
8.3 The beam-splitter and coherent states
8.4 The beam-splitter with two photons
8.5 The Hong-Ou-Mandel experiment
8.6 The Mach-Zehnder set-up
8.7 A quantum bomb detector
9. Quantum entanglement and some applications
9.1 Introduction to Quantum measurement
9.2 Quantum cryptography
9.2.1 BB84 protocol
9.2.2 B92 protocol
9.2.3 Ekert protocol
9.3 Quantum teleportation
9.4 Quantum dense coding
9.5 Quantum repeaters and Quantum memory
9.6 Entanglement distillation
9.7 Non-locality and the Einstein, Podolsky, and Rosen paradox
9.8 Bell's inequalities
9.9 Generalised measurement (POVM)
9.10 Example POVM problems
10. Decay of quantum systems
10.1 Introduction to decoherence
10.2 The bath model
10.3 Derivation of the master equation
10.4 Examples of master equations and decaying quantum systems
10.4.1 Decay of an atom
10.4.2 Decay of a number state
10.4.3 Decay of a coherent state
10.4.4 Decay of a "Schrödinger cat"
10.4.5 Master equation for dephasing
10.5 Unravelling a master equation
10.6 Measurement and the environment
10.7 Theory of effective modes
10.8 Measure of non-Markovianity
11. Cooling and trapping atoms with photons
11.1 Kinetic action of light on matter
11.2 Doppler cooling
11.3 Trapped atoms
11.4 Trapped ions
11.4.1 Paul trap and Penning trap
11.4.2 Lamb-Dicke limit
11.4.3 Cooling trapped ions
12. Measures of quantum information and entanglement
12.1 Quantum information and quantum entropy
12.2 Mutual information and the Araki-Lieb inequality
12.3 Concurrence
12.4 The tangle
12.5 Global entanglement
12.6 Quantum discord
13. Quantum gates
13.1 Quantum gates
13.2 Rotations and one-qubit gates
13.3 Two qubit gates
13.4 Three or more qubit gates
14. Quantum computing: algorithms
15. Physical systems for quantum computing
15.1 Ion traps
15.2 Linear optical Quantum computing
15.3 Cavity QED for Quantum computing
15.4 Circuit QED and superconducting qubits
15.5 Condensed matter: quantum dots
15.6 NMR Quantum computing
15.7 Cluster state Quantum computing
15.8 Continuous variable Quantum computing
16. Reference section
16.1 Introduction to the reference section
16.2 Additional theorems
16.3 Single mode states
16.3.1 Number state
16.3.2 Coherent state
16.3.3 Squeezed vacuum state
16.3.4 Squeezed coherent state
16.3.5 Thermal state
16.3.6 Displaced number state
16.3.7 Phase state
16.3.8 Even and odd coherent states
16.3.9 Yurke-Stoler cat state
16.3.10 Single mode binomial state
16.4 Multi-mode states
16.4.1 The Bell states
16.4.2 Werner state for 2 qubits
16.4.3 The X-state for 2 qubits
16.4.4 Two-mode squeezed state
16.4.5 Two-mode binomial state
16.4.6 GHZ state for 3 qubits
16.4.7 GHZ state for N qubits
16.4.8 The W-state for N qubits
16.5 Spin states and additional theorems for spins
16.5.1 Sz eigenstates and ladder operators
16.5.2 Spin coherent states
16.5.3 Spin squeezed states

Authors

Barry M. Garraway University of Sussex, UK.