Preface to the German Edition.

1 The Mathematical Framework.

1.1 Hilbert Vector Space.

1.2 Liouville Operator Space.

1.3 The Elements of Probability Theory.

1.4 Complementary Topics and Further Reading.

1.5 Problems for Chapter 1.

2 Basic Concepts of Quantum Theory.

2.1 First Version of the Postulates (pure states of isolated quantum systems).

2.2 Outlook.

2.3 Manipulation of the Evolution of the States by Projective Measurements.

2.4 The Structure of Physical Theories.

2.5 Interpretations of Quantum Theory and Physical Reality.

2.6 Complementary Topics and Further Reading.

3 The Simplest Quantum Systems: Qubits.

3.1 Pauli Operators.

3.2 Visualisation of Qubits on the Bloch Sphere.

3.3 Visualisation of the Measurement Dynamics and the Unitary Dynamics.

3.4 Quantum Gates for Single Qubit Systems.

3.5 Spin-1/2.

3.6 Photon Polarisations.

3.7 Single Photons in a Beam Splitter and in an Interferometer.

3.8 Locating a Bomb Without Exploding It by Using a Null Measurement.

3.9 Complementary Topics and Further Reading.

3.10 Problems for Chapter 3.

4 Mixed States and the Density Operator.

4.1 Density Operators for a Given Ensemble (Statistical Mixture).

4.2 The Generalised Quantum State.

4.3 Different Ensemble Decompositions of a Density Operator and the Ignorance Interpretation.

4.4 Density Operators of Qubits.

4.5 Complementary Topics and Further Reading.

4.6 Problems for Chapter 4.

5 Shannon’s Entropy and Classical Information.

5.1 Definition and Properties.

5.2 Shannon’s Theorem.

5.3 Classical Information.

5.4 Classical Relative Entropy.

5.5 Mutual Information as a Measure of the Correlation between Two Messages.

5.6 Complementary Topics and Further Reading.

5.7 Problems for Chapter 5.

6 The von Neumann Entropy and Quantum Information.

6.1 The Quantum Channel and Quantum Entropy.

6.2 Qubits as the Unit of Quantum Information.

6.3 Properties.

6.4 The Interfaces of Preparation and Measurement.

6.5 Quantum Information.

6.6 Complementary Topics and Further Reading.

6.7 Problems for Chapter 6.

7 Composite Systems.

7.1 Subsystems.

7.2 The Product Hilbert Space.

7.3 The Fundamentals of the Physics of Composite Quantum Systems.

7.4 Manipulationson aSubsystem.

7.5 Separate Manipulations on both Subsystems.

7.6 The Unitary Dynamics of Composite Systems.

7.7 A First Application of Entanglement: a Conjuring Trick.

7.8 Quantum Gates for Multiple Qubit Systems.

7.9 Systems of Identical Particles.

7.10 Complementary Topics and Further Reading.

7.11 Problems for Chapter 7.

8 Entanglement.

8.1 Correlations andEntanglement.

8.2 Outlook.

8.3 Entangled Pure States.

8.4 The PPT Criterion for the Entanglement of Mixtures.

8.5 The Production of Entangled States.

8.6 The No-Cloning Theorem Prevents Transfer of Information Faster than the Velocity.of.Light.

8.7 Marking States by Entanglement.

8.8 Complementary Topics and Further Reading.

8.9 Problems for Chapter 8.

9 Correlations and Non-Local Measurements.

9.1 Entropies and the Correlations of Composite Quantum Systems.

9.2 Non-Local Measurements.

9.3 Complementary Topics and Further Reading.

9.4 Problems for Chapter 9.

10 There is no (Local-Realistic) Alternative to Quantum Theory.

10.1 EPR Experiments and Their Quantum-mechanical Explanation.

10.2 Correlated Gloves.

10.3 Local Realism.

10.4 Hidden Variables, Bell Inequalities and Contradictions of Experiments.

10.5 Separable Mixtures Obey the Bell Inequality.

10.6 Entanglement Witnesses.

10.7 3-Particle Entanglement and Quantum Locality.

10.8 Complementary Topics and Further Reading.

10.9 Problems for Chapter 10.

11 Working with Entanglement.

11.1 Quantum Cryptography.

11.2 One Qubit Transmits Two Bits (Dense Coding).

11.3 Quantum Teleportation.

11.4 Entanglement Swapping.

11.5 Spooky Action into the Past?

11.6 Entanglement Distillation.

11.7 A Measure of Entanglement for Mixtures: Entanglement of Formation and Concurrence.

11.8 Complementary Topics and Further Reading.

11.9 Problems for Chapter 11.

12 The Quantum Computer.

12.1 Registers and Networks.

12.2 Functional Computation.

12.3 Quantum Parallelism.

12.4 Two Simple Quantum Algorithms.

12.5 Grover’s Search Algorithm.

12.6 Shor’s Factorisation Algorithm.

12.7 Quantum Error Correction Using Non-local Measurements.

12.8 The Components of the Quantum Computer.

12.9 Complementary Topics and Further Reading.

12.10 Problems for Chapter 12.

13 Generalised Measurements, POVM.

13.1 The Function of a Generalised Dynamics of Open Quantum Systems.

13.2 The Non-optimal Stern-Gerlach Experiment and Generalised Measurements.

13.3 Generalised Measurements.

13.4 POVM Measurements.

13.5 Complementary Topics and Further Reading.

13.6 Problems for Chapter 13.

14 The General Evolution of an Open Quantum System and Special Quantum Channels.

14.1 Quantum Operations and their Operator-Sum Decompositions.

14.2 The Master Equation.

14.3 Completely General Selective Measurements and POVM.

14.4 Quantum Channels.

14.5 The Scenario and the Rules of Quantum Theory Revisited.

14.6 Complementary Topics and Further Reading.

14.7 Problems for Chapter 14.

15 Decoherence and Approaches to the Description of the Quantum Measurement Process.

15.1 Channels which Produce Decoherence.

15.2 Environment-Induced Decoherence.

15.3 The Quantum Measurement Process.

15.4 Has the Problem of Measurements been Solved?

15.5 The Many-Worlds Interpretation.

15.6 Complementary Topics and Further Reading.

15.7 Problems for Chapter 15.

16 Two Implementations of Quantum Operations.

16.1 The Operator-Sum Decomposition.

16.2 The Unitary Implementation of Quantum Operations.

16.3 Implementation of a Completely General Selective Measurement by Unitary Transformation and Projection.

16.4 Complementary Topics and Further Reading.

16.5 Problems for Chapter 16.

References.

Reference categories.

Bibliography.

Subject Index.