Quantum Cryptography

How can you tell a secret when everyone is able to listen in? In this course, you will learn how to use quantum effects, such as quantum entanglement and uncertainty, to implement cryptographic tasks with levels of security that are impossible to achieve classically.

This interdisciplinary course is an introduction to the exciting field of quantum cryptography, developed in collaboration between QuTech at Delft University of Technology and the California Institute of Technology.

By the end of the course you will

• Be armed with a fundamental toolbox for understanding, designing and analyzing quantum protocols.
• Understand quantum key distribution protocols.
• Understand how untrusted quantum devices can be tested.
• Be familiar with modern quantum cryptography – beyond quantum key distribution.

This course assumes a solid knowledge of linear algebra and probability at the level of an advanced undergraduate. Basic knowledge of elementary quantum information (qubits and simple measurements) is also assumed, but if you are completely new to quantum information additional videos are provided for you to fill in any gaps.

Optional Background Videos:

• Qubits
• Quantum gates
• Measuring qubits in a basis

Week 1: Quantum tools and a first protocol

• Introduction and overview
• Fundamental concepts of quantum information: pure and mixed quantum states, the partial trace, classical-quantum states, generalized measurements
• Encrypting quantum bits with the quantum one-time pad

Week 2: The power of entanglement

• Separable states, entangled states and purification
• Sharing a classical secret using quantum states
• Looking ahead to quantum key distribution: verifying entanglement using a Bell experiment
• Monogamy of entanglement

Week 3: Quantifying information

• What it means to be ignorant: trace distance and its use in security definitions
• The (min)-entropy
• Uncertainty principles as a guessing game

Week 4: From imperfect information to (near) perfect security

• Introduction to privacy amplification
• Strong randomness extractors
• Randomness extraction using two-universal hashing
• A construction of two-universal hash functions

Week 5: Distributing keys

• Introduction to key distribution: the challenge of being correct and secure
• Key distribution over a noisy channel

Guest video: David Elkouss (QuTech, TU Delft) – Practical error correction in key distribution protocols

Week 6: Quantum key distribution protocols

• BB84 Protocol
• Warmup: Security against a classical eavesdropper
• E91 Protocol: purifying protocols using entanglement
• Quantum key distribution: definitions and concepts

Guest video: Nicolas Gisin (University of Geneva) – Quantum key distribution in practice

Week 7: Quantum cryptography using untrusted devices

• Introduction to device-independent quantum cryptography
• Testing devices using a Bell experiment
• Security of device-independent quantum key distribution against collective attacks

Guest video: Ronald Hanson (QuTech, TU Delft) – The first loophole free Bell experiment

Week 8: Quantum cryptography beyond key-distribution

• Introduction and overview
• Two-party cryptography: bit commitment and oblivious transfer
• Impossibility of bit commitment
• Weak commitments and coin tossing

Week 9: Perfect security from physical assumptions

• The noisy storage model
• A simple protocol for bit commitment in the noisy-storage model
• Security from quantum uncertainty
• A universal primitive: weak string erasure

Week 10: Further topics

• Position verification from weak string erasure
• Sharing a quantum secret
• Secure computations on a remote quantum computer