Quantum Information Processing is a young and rapidly growing field of research at the intersection of physics, mathematics, and computer science. Its ultimate goal is to harness quantum physics to conceive—and ultimately build—"quantum" computers that would dramatically overtake the capabilities of today's "classical" computers. One example of the power of a quantum computer is its ability to efficiently find the prime factors of a larger integer, thus shaking the supposedly secure foundations of standard encryption schemes.

This comprehensive textbook on the rapidly advancing field introduces readers to the fundamental concepts of information theory and quantum entanglement, taking into account the current state of research and development. It thus covers all current concepts in quantum computing, both theoretical and experimental, before moving on to the latest implementations of quantum computing and communication protocols. With its series of exercises, this is ideal reading for students and lecturers in physics and informatics, as well as experimental and theoretical physicists, and physicists in industry.

 

Preface.

List of Contributors.

I Classical Information Theory.

1 Classical Information Theory and Classical Error Correction (M. Grassl).

1.1 Introduction.

1.2 Basics of Classical Information Theory.

1.3 Linear Block Codes.

1.4 Further Aspects.

References.

2 Computational Complexity (S. Mertens).

2.1 Basics.

2.2 Algorithms and Time Complexity.

2.3 Tractable Trails: The Class P.

2.4 Intractable Itineraries: The class NP.

2.5 Reductions and NP-completeness.

2.6 P vs. NP.

2.7 Optimization.

2.8 Complexity Zoo.

References.

II Foundation of Quantum Information Theory.

3 Discrete Quantum States versus Continuous Variables (J. Eisert).

3.1 Introduction.

3.2 Finite-dimensional quantum systems.

3.3 Continuous-variables.

References.

4 Approximate Quantum Cloning (D. Bruß and C. Macchiavello).

4.1 Introduction.

4.2 The No-Cloning Theorem.

4.3 State-Dependent Cloning.

4.4 Phase Covariant Cloning.

4.5 Universal Cloning.

4.6 Asymmetric Cloning.

4.7 Probabilistic Cloning.

4.8 Experimental Quantum Cloning.

4.9 Summary and Outlook.

References.

5 Channels and Maps (M. Keyl and R. F. Werner).

5.1 Introduction.

5.2 Completely Positive Maps.

5.3 The Jamiolkowski Isomorphism.

5.4 The Stinespring Dilation Theorem.

5.5 Classical Systems as a Special Case.

5.6 Examples.

References.

6 Quantum Algorithms (J. Kempe).

6.1 Introduction.

6.2 Precursors.

6.3 Shor’s Factoring Algorithm.

6.4 Grover’s Algorithm.

6.5 Other Algorithms.

6.6 Recent Developments.