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Syllabus

Since this is an experimental course which is being taught for the first time, the syllabus is subject to change. Below is its rough summary though I expect that we will not be able to cover all the listed topics.

Quantum Cryptography

Weeks 1/2/3: Quantum tools and a first cryptographic protocol

  • Qubits
  • Density matrices
  • Measurements
  • Partial trace
  • Secure message transmission
  • Classical and quantum one-time pad

Weeks 3/4: The power of entanglement

  • Introduction to entanglement
  • Purifications
  • Secret sharing
  • Bell nonlocality
  • The monogamy of entanglement

Week 4/5: Quantifying information

  • Measures of closeness of two quantum states: trace distance and fidelity
  • Measures of uncertainty: von Neumann and min- entropies
  • Uncertainty principle as a guessing game

Week 5/6: From imperfect information to (near) perfect security

  • Privacy amplification
  • Randomness extractors

Week 6/7: Distributing keys and quantum key distribution protocols

  • Secure key distribution
  • Information reconciliation
  • The BB84 quantum key distribution protocol
  • Purifying protocols using entanglement
  • Security from tripartite uncertainty relations

Week 7/8: Quantum cryptography using untrusted devices

  • Testing devices using a Bell experiment
  • Device independent quantum key distribution

Quantum Communication

Week 9/10: Generating remote entanglement

  • Encoding quantum information in light
  • Quantum teleportation
  • Entanglement swapping
  • Heralded entanglement generation
  • Overview of physical implementations
  • Satellite-based quantum communication

Week 10: Distilling entanglement

  • Filtering scheme
  • Entanglement distillation from 2 to 1 copy

Week 11: Overcoming photon loss: heralded repeater chains

  • Nested repeater chain
  • Repeater chain with limited memory coherence time

Week 12: Quantum repeater generations with error correction

  • Basic quantum error correction tools
  • 2nd generation repeaters: protecting entanglement swapping through error correction
  • 3rd generation repeaters: overcoming photon loss through error correction

Week 13: Limits to sending quantum information

  • Quantum channel capacities
  • When does a repeater repeat?