Category:Handbook of Quantum Information

The Handbook of Quantum Information is an encyclopaedia of everything quantum!

Sections

1. Mathematical Structure
2. Quantum States
3. Evolution and Operations
4. Entanglement
5. Quantum Information Theory
6. Quantum Communication
7. Quantum Cryptography
8. Quantum Computation
9. Quantum Algorithms
10. Quantum Error Correction
11. Quantum Ladder
12. Physical Realisations
13. Miscellaneous

Table of contents

1. Mathematical Structure
   1. Hilbert spaces
   2. Bra-ket notation
   3. Density matrix
   4. Ensemble
   5. States
   6. Tensor products
   7. Bipartite states and Schmidt Decomposition
   8. Observables and measurements
   9. Operators
      1. Symmetric operator
      2. Hermitian matrix
      3. Self-adjoint operator
      4. Positive operator
      5. Projector
   10. purification
   11. Stinespring dilation
   12. Kraus decomposition
   13. Bit
   14. Random variable
2. Quantum States
   1. qubits and qudits
   2. Bloch sphere
   3. pure states
   4. mixed states
   5. Ensembles
   6. Distance measures between states
      1. Fidelity
      2. Trace distance
   7. States with well known properties
      1. Bell states
      2. Singlet
      3. GHZ
      4. W-state
      5. Bell-diagonal states
      6. Werner states
      7. Isotropic states
      8. Matrix product states
   8. Tomography
3. Evolution and Operations
   1. Unitarity and time evolution
   2. Channels (CP maps)
   3. The Church of the larger Hilbert space
   4. Measurements and preparations
   5. State transformations criteria (majorization)
   6. Quantum gates
   7. Frequently used gates
      1. Hadamard
      2. CNOT
      3. Bell measurement
   8. Geometric (holonomic) gates
4. Entanglement
   1. separable and entangled states
      1. Separability criteria
         1. PPT criterion
   2. Bell's theorem
   3. Distant laboratories scenario
      1. LOCC operations
      2. Separable operations
      3. PPT operations
   4. Entanglement measures
      1. Operational measures
      2. Axiomatic Approach
      3. Entropy of entanglement
      4. Entanglement cost
      5. Distillable entanglement
      6. Squashed entanglement
      7. Entanglement of formation
      8. Negativity
      9. Logarithmic negativity
      10. Relative entropy of entanglement
   5. Bound entanglement
      1. Activation of bound entanglement
      2. Bound entangled states
   6. Entanglement of particular states
      1. Bell diagonal states
      2. Werner states
      3. Isotropic states
      4. Graph states
      5. Stabilizer states
   7. Monogamy of entanglement
   8. Multipartite entanglement
      1. MREG
      2. Entanglement of Assistance
5. Quantum Information Theory
   1. What is information?
      1. Classical information
         1. Classical Entropy Measures
         2. Classical relative entropy
         3. Shannon's noiseless coding theorem
         4. Mutual informatioin
         5. Conditional entropy
         6. Venn diagram
      2. Quantum information
         1. Quantum mutual information
         2. Quantum partial information
         3. Quantum relative entropy
         4. Coherent information
         5. Strong sub-additivity
         6. Entanglement of purification
      3. Quantum state compression
   2. How much information is contained in a quantum state: the Holevo-Nayak theorem
      1. The Holevo-Nayak bound
      2. The Holevo bound
      3. Super-dense coding
   3. The no-cloning theorem
6. Quantum Communication
   1. Teleportation
   2. Channels
      1. Classical channel
      2. Quantum channel
      3. Entanglement-breaking channel
   3. Classical channel capacity
      1. entanglement assisted classical capacity
   4. Quantum channel capacity
   5. Coherent information
   6. Enhancement of channel capacities with entanglement
   7. Additivity
7. Quantum Cryptography
   1. Quantum key distribution
   2. Communication protocols between mistrustful parties
      1. Bit commitment
      2. Coin tossing
         1. Strong coin tossing
      3. Oblivious transfer
      4. Secure two party classical computation: overview
      5. Quantum Secret Sharing
8. Quantum Computation
   1. Models of quantum computation
      1. Circuit model
         1. Universality
         2. Approximate universality
         3. One Qubit Gates
         4. Two Qubit Gates
         5. Multi Qubit Gates
      2. Turing machines
      3. Adiabatic computation
      4. KLM
      5. One-way computation
      6. Quantum lambda calculus
      7. Quantum cellular automata
      8. Topological computation
   2. Computational complexity
      1. BQP
9. Quantum Algorithms
   1. Deutsch-Josza algorithm
   2. Grover's search algorithm
   3. Shor's factoring algorithm
   4. The hidden subgroup problem
   5. Graph isomorphism
   6. Computing the Jones Polynomial
   7. Element distinctness (Ambianis's Algorithm
   8. Quantization of Classical walk based algorithms (e.g. Szegedy)
   9. Graph traversal (Childs et. al.)
10. Quantum Error Correction
    1. Decoherence
    2. Decoherence-free subspaces (error avoiding)
    3. Error correction
    4. Fault tolerance
       1. Concatenation of quantum codes
       2. Anyons
11. Physical Realisations
    1. Linear optics
       1. single photon sources
       2. KLM scheme
    2. Cavity QED
    3. Photonic crystals
    4. Ion traps
    5. Optical lattices
       1. Bose Einstein condensates
       2. Mott insulator
    6. Superconducting qubits
       1. Superconductivity
       2. Flux qubits
       3. Charge qubits
    7. Liquid-state NMR
    8. Solid-state NMR
    9. Quantum dots
       1. Spin qubits
       2. Charge qubits
12. Miscellaneous
    1. Quantum Sock Theory