Entangled Systems: New Directions in Quantum Physics by Jürgen Audretsch Softcover - 357 pages Shipped in CLICK HERE Cat.# JW-NQP1 $ 94.50 BUY Published:  2007   ISBN:  9783527406845

An introductory textbook for advanced students of physics, chemistry and computer science, covering an area of physics that has lately witnessed rapid expansion. The topics treated here include quantum information, quantum communication, quantum computing, teleportation and hidden parameters, thus imparting not only a well-founded understanding of quantum theory as such, but also a solid basis of knowledge from which readers can follow the rapid development of the topic or delve deeper into a more specialized branch of research. Commented recommendations for further reading as well as end-of-chapter problems help the reader to quickly access the theoretical basics of future key technologies.

Table of Contents:

Preface to the English Edition
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 a Subsystem
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 and Entanglement
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

Quantum Theory of Optical Coherence: Selected Papers and Lectures by Roy J. Glauber Hardcover - 656 pages Shipped in CLICK HERE Cat.# JW-NQP2 $197.20 BUY Published:  2007   ISBN:  9783527406876

A summary of the pioneering work of Glauber in the field of optical coherence phenomena and photon statistics, this book describes the fundamental ideas of modern quantum optics and photonics in a tutorial style. It is thus not only intended as a reference for researchers in the field, but also to give graduate students an insight into the basic theories of the field.

Written by the Nobel Laureate himself, the concepts described in this book have formed the basis for three further Nobel Prizes in Physics within the last decade.

Table of Contents:

1. The Quantum Theory of Optical Coherence

1.1 Introduction
1.2 Elements of Field Theory
1.3 Field Correlations
1.4 Coherence
1.5 Coherence and Polarization

2. Optical Coherence and Photon Statistics

2.1 Introduction
2.1.1 Classical Theory
2.2 Interference Experiments
2.3 Introduction of Quantum Theory
2.4 The One-Atom Photon Detector
2.5 The n-Atom Photon Detector
2.6 Properties of the Correlation Functions
2.6.1 Space and Time Dependence of the Correlation Functions
2.7 Diffraction and Interference
2.7.1 Some General Remarks on Interference
2.7.2 First-Order Coherence
2.7.3 Fringe Contrast and Factorization
2.8 Interpretation of Intensity Interferometer Experiments
2.8.1 Higher Order Coherence and Photon Coincidences
2.8.2 Further Discussion of Higher Order Coherence
2.8.3 Treatment of Arbitrary Polarizations
2.9 Coherent and Incoherent States of the Radiation Field
2.9.1 Introduction
2.9.2 Field-Theoretical Background
2.9.3 Coherent States of a Single Mode
2.9.4 Expansion of Arbitrary States in Terms of Coherent States
2.9.5 Expansion of Operators in Terms of Coherent State Vectors
2.9.6 General Properties of the Density Operator
2.9.7 The P Representation of the Density Operator
2.9.8 The Gaussian Density Operator
2.9.9 Density Operators for the Field
2.9.10 Correlation and Coherence Properties of the Field
2.10 Radiation by a Predetermined Charge–Current Distribution
2.11 Phase-Space Distributions for the Field
2.11.1 The P Representation and the Moment Problem
2.11.2 A Positive-Definite “Phase Space Density”
2.11.3 Wigner’s “Phase Space Density”
2.12 Correlation Functions and Quasiprobability Distributions
2.12.1 First Order Correlation Functions for Stationary Fields
2.12.2 Correlation Functions for Chaotic Fields
2.12.3 Quasiprobability Distribution for the Field Amplitude
2.12.4 Quasiprobability Distribution for the Field Amplitudes at Two Space-Time Points
2.13 Elementary Models of Light Beams
2.13.1 Model for Ideal Laser Fields
2.13.2 Model of a Laser Field With Finite Bandwidth
2.14 Interference of Independent Light Beams
2.15 Photon Counting Experiments

References

3. Correlation Functions for Coherent Fields

3.1 Introduction
3.2 Correlation Functions and Coherence Conditions
3.3 Correlation Functions as Scalar Products
3.4 Application to Higher Order Correlation Functions
3.5 Fields With Positive-Definite P Functions

References

4. Density Operators for Coherent Fields

4.1 Introduction
4.2 Evaluation of the Density Operator
4.3 Fully Coherent Fields
4.4 Unique Properties of the Annihilation Operator Eigenstates

5. Classical Behavior of Systems of Quantum Oscillators

6. Quantum Theory of Parametric Amplification I

6.1 Introduction
6.2 The Coherent States and the P Representation
6.3 Model of the Parametric Amplifier
6.4 Reduced Density Operator for the A Mode
6.5 Initially Coherent State: P Representation for the A Mode
6.6 Initially Coherent State; Moments, Matrix Elements, and Explicit Representation for pA(t)
6.7 Solutions for an Initially Chaotic B Mode
6.8 Solution for Initial n-Quantum State of A Mode; B Mode Chaotic
6.9 General Discussion of Amplification With B Mode Initially Chaotic
6.10 Discussion of P Representation: Characteristic Functions Initially Gaussian
6.11 Some General Properties of P(α, t)

7. Quantum Theory of Parametric Amplification II

7.1 Introduction
7.2 The Two-Mode Characteristic Function
7.3 The Wigner Function
7.4 Decoupled Equations of Motion
7.5 Characteristic Functions Expressed in Terms of Decoupled Variables
7.6 W and P Expressed in Terms of Decoupled Variables
7.7 Results for Chaotic Initial States
7.8 Correlations of the Mode Amplitudes

References

8. Photon Statistics

8.1 Introduction.
8.2 Classical Theory
8.3 Quantum Theory: Introduction
8.4 Intensity and Coincidence Measurements
8.5 First and Higher Order Coherence
8.6 The Coherent States
8.7 Expansions in Terms of the Coherent States
8.8 Characteristic Functions and Quasiprobability Densities
8.9 Some Examples
8.10 Photon Counting Distributions

9. Ordered Expansions in Boson Amplitude Operators

9.1 Introduction
9.2 Coherent States and Displacement Operators
9.3 Completeness of Displacement Operators
9.4 Ordered Power-Series Expansions
9.5 s-Ordered Power-Series Expansions
9.6 Integral Expansions for Operators
9.7 Correspondences Between Operators and Functions
9.8 Illustration of Operator–Function Correspondences

10. Density Operators and Quasiprobability Distributions

10.1 Introduction
10.2 Ordered Operator Expansions
10.3 The P Representation
10.4 Wigner Distribution
10.5 The Function (α, p, α)
10.6 Ensemble Averages and s Ordering
10.7 Examples of the General Quasiprobability Function W (α, s)
10.8 Analogy with Heat Diffusion
10.9 Time-Reversed Heat Diffusion and W (α, s)
10.10 Properties Common to all Quasiprobability Distributions

11. Coherence and Quantum Detection

11.1 Introduction
11.2 The Statistical Properties of the Electromagnetic Field
11.3 The Ideal Photon Detector
11.4 Correlation Functions and Coherence
11.5 Other Correlation Functions
11.6 The Coherent States
11.7 Expansions in Terms of Coherent States
11.8 A Few General Observations
11.9 The Damped Harmonic Oscillator
11.10 The Density Operator for the Damped Oscillator
11.11 Irreversibility and Damping
11.12 The Fokker–Planck and Bloch Equations
11.13 Theory of Photodetection. The Photon Counter Viewed as a Harmonic Oscillator
11.14 The Density Operator for the Photon Counter

12. Quantum Theory of Coherence

12.1 Introduction
12.2 Classical Theory
12.3 Quantum Theory
12.4 Intensity and Coincidence Measurements
12.5 Coherence
12.6 Coherent States
12.7 The P Representation
12.8 Chaotic States
12.9 Wavepacket Structure of Chaotic Field

13. The Initiation of Superfluorescence

13.1 Introduction
13.2 Basic Equations for a Simple Model
13.3 Onset of Superfluorescence

14. Amplifiers, Attenuators and Schrodingers Cat

14.1 Introduction: Two Paradoxes
14.2 A Quantum-Mechanical Attenuator: The Damped Oscillator
14.3 A Quantum Mechanical Amplifier
14.4 Specification of Photon Polarization States
14.5 Measuring Photon Polarizations
14.6 Use of the Compound Amplifier
14.7 Superluminal Communication?
14.8 Interference Experiments and Schrodinger’s Cat

15. The Quantum Mechanics of Trapped Wavepackets

15.1 Introduc
15.2 Equations of Motion and Their Solutions
15.3 The Wave Functions
15.4 Periodic Fields and Trapping
15.5 Interaction With the Radiation Field
15.6 Sum Rules
15.7 Radiative Equilibrium and Instability

16. Density Operators for Fermions

16.1 Introduction
16.2 Notation
16.3 Coherent States for Fermions
16.3.1 Displacement Operators
16.3.2 Coherent States
16.3.3 Intrinsic Descriptions of Fermionic States
16.4 Grassmann Calculus
16.4.1 Differentiation
16.4.2 Even and Odd Functions
16.4.3 Product Rule
16.4.4 Integration
16.4.5 Integration by Parts
16.4.6 Completeness of the Coherent States
16.4.7 Completeness of the Displacement Operators
16.5 Operators
16.5.1 The Identity Operator
16.5.2 The Trace
16.5.3 Physical States and Operators
16.5.4 Physical Density Operators
16.6 Functions and Fourier Transforms
16.7 Operator Expansions
16.8 Characteristic Functions
16.8.1 The s-Ordered Characteristic Function
16.9 s-Ordered Expansions for Operators
16.10 Quasiprobability Distributions
16.11 Mean Values of Operators
16.12 P Representation
16.13 Correlation Functions for Fermions
16.14 Chaotic States of the Fermion Field
16.15 Correlation Functions for Chaotic Field Excitations
16.16 Fermion-Counting Experiments
16.17 Some Elementary Examples
16.17.1 The Vacuum State
16.17.2 A Physical Two-Mode Density Operator

Index

Elements of Quantum Information by Wolfgang P. Schleich, and Herbert Walther Hardcover - 528 pages Shipped in CLICK HERE Cat.# JW-NQP3 $212.70 BUY Published:  2007   ISBN:  9783527407255

By merging computer science, physics, mathematics and engineering, this monograph takes into account the current state of research and development to introduce readers to the use of quantum mechanics as a resource for high-potential modern applications.

Table of Contents:

Preface to the Book
Preface to the Journal
List of Contributors

1. The Deterministic Generation of Photons by Cavity Quantum Electrodynamics

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

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

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 a Well-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

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

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

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

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

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

9.1 Introduction
9.2 Experimental Setup and Cold Atom Preparation
9.3 Spectroscopy of Rydberg States, 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

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

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

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?

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

14.1 Introduction
14.2 Theory
14.3 Experiment
14.4 Conclusion

References

15. Free Space Quantum Key Distribution: Towards a Real Life Application

15.1 Introduction
15.2 Setup
15.3 Conclusion

References

16. Continuous Variable Entanglement Between Frequency Modes

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

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

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

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

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

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

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