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Quantum Processes Systems, and Information

Book Description

A new and exciting approach to the basics of quantum theory, this undergraduate textbook contains extensive discussions of conceptual puzzles and over 800 exercises and problems. Beginning with three elementary 'qubit' systems, the book develops the formalism of quantum theory, addresses questions of measurement and distinguishability, and explores the dynamics of quantum systems. In addition to the standard topics covered in other textbooks, it also covers communication and measurement, quantum entanglement, entropy and thermodynamics, and quantum information processing. This textbook gives a broad view of quantum theory by emphasizing dynamical evolution, and exploring conceptual and foundational issues. It focuses on contemporary topics, including measurement, time evolution, open systems, quantum entanglement, and the role of information.

Table of Contents

  1. Cover
  2. Half Title
  3. Title Page
  4. Copyright
  5. Contents
  6. Preface
  7. 1. Bits and quanta
    1. 1.1 Information and bits
    2. 1.2 Wave–particle duality
    3. Problems
  8. 2. Qubits
    1. 2.1 The photon in the interferometer
    2. 2.2 Spin 1/2
    3. 2.3 Two-level atoms
    4. 2.4 Qubits and isomorphism
    5. Problems
  9. 3. States and observables
    1. 3.1 Hilbert space
    2. 3.2 Operators
    3. 3.3 Observables
    4. 3.4 Adjoints
    5. 3.5 Eigenvalues and eigenvectors
    6. Problems
  10. 4. Distinguishability and information
    1. 4.1 Quantum communication
    2. 4.2 Distinguishability
    3. 4.3 The projection rule and its limitations
    4. 4.4 Quantum cryptography
    5. 4.5 The uncertainty relation
    6. Problems
  11. 5. Quantum dynamics
    1. 5.1 Unitary evolution
    2. 5.2 The Schrödinger equation
    3. 5.3 Quantum clock-making
    4. 5.4 Operators and symmetries
    5. Problems
  12. 6. Entanglement
    1. 6.1 Composite systems
    2. 6.2 Interaction and entanglement
    3. 6.3 A 4π world
    4. 6.4 Conditional states
    5. 6.5 EPR
    6. 6.6 Bell’s theorem
    7. 6.7 GHZ
    8. Problems
  13. 7. Information and ebits
    1. 7.1 Decoding and distinguishability
    2. 7.2 The no-cloning theorem
    3. 7.3 Ebits
    4. 7.4 Using entanglement
    5. 7.5 What is quantum information?
    6. Problems
  14. 8. Density operators
    1. 8.1 Beyond state vectors
    2. 8.2 Matrix elements and eigenvalues
    3. 8.3 Distinguishing mixed states
    4. 8.4 The Bloch sphere
    5. 8.5 Time evolution
    6. 8.6 Uniform density operators
    7. 8.7 The canonical ensemble
    8. Problems
  15. 9. Open systems
    1. 9.1 Open system dynamics
    2. 9.2 Informationally isolated systems
    3. 9.3 The Lindblad equation
    4. 9.4 Heat and work
    5. 9.5 Measurements on open systems
    6. 9.6 Information and open systems
    7. Problems
  16. 10. A particle in space
    1. 10.1 Continuous degrees of freedom
    2. 10.2 Continuous observables
    3. 10.3 Wave packets
    4. 10.4 Reflection and recoil
    5. 10.5 More dimensions of space
    6. 10.6 How not to think about ψ
    7. Problems
  17. 11. Dynamics of a free particle
    1. 11.1 Dynamics in 1-D
    2. 11.2 Free particles in 1-D
    3. 11.3 Particle on a circle
    4. 11.4 Particle in a box
    5. 11.5 Quantum billiards
    6. Problems
  18. 12. Spin and rotation
    1. 12.1 Spin-s systems
    2. 12.2 Orbital angular momentum
    3. 12.3 Rotation
    4. 12.4 Adding spins
    5. 12.5 Isospin
    6. Problems
  19. 13. Ladder systems
    1. 13.1 Raising and lowering operators
    2. 13.2 Oscillators
    3. 13.3 Coherent states
    4. 13.4 Thermal states of a ladder system
    5. Problems
  20. 14. Many particles
    1. 14.1 Two-particle wave functions
    2. 14.2 Center of mass and relative coordinates
    3. 14.3 Identical particles
    4. 14.4 Energy levels
    5. 14.5 Exchange effects
    6. 14.6 Occupation numbers
    7. Problems
  21. 15. Stationary states in 1-D
    1. 15.1 Wave functions and potentials
    2. 15.2 Reflecting, scattering, and bound states
    3. 15.3 A potential step
    4. 15.4 Scattering from a square barrier
    5. 15.5 Bound states in a square well
    6. 15.6 The variational method
    7. 15.7 Parameters and scaling
    8. Problems
  22. 16. Bound states in 3-D
    1. 16.1 Central potentials
    2. 16.2 The isotropic oscillator
    3. 16.3 Hydrogen
    4. 16.4 Some expectations
    5. Problems
  23. 17. Perturbation theory
    1. 17.1 Shifting the energy levels
    2. 17.2 Dealing with degeneracy
    3. 17.3 Perturbing the dynamics
    4. 17.4 Cross-sections
    5. Problems
  24. 18. Quantum information processing
    1. 18.1 Quantum circuits
    2. 18.2 Computers and algorithms
    3. 18.3 Nuclear spins
    4. 18.4 NMR in the real world
    5. 18.5 Pulse sequences
    6. Problems
  25. 19. Classical and quantum entropy
    1. 19.1 Classical entropy
    2. 19.2 Classical data compression
    3. 19.3 Quantum entropy
    4. 19.4 Quantum data compression
    5. 19.5 Entropy and thermodynamics
    6. 19.6 Bits and work
    7. Problems
  26. 20. Error correction
    1. 20.1 Undoing errors
    2. 20.2 Classical communication and error correction
    3. 20.3 Quantum communication and error correction
    4. 20.4 Error-correcting codes
    5. 20.5 Information and isolation
    6. Problems
  27. Appendix A: Probability
  28. Appendix B: Fourier facts
  29. Appendix C: Gaussian functions
  30. Appendix D: Generalized evolution
  31. Index