This course introduces the fundamental concepts of quantum communication and computing. Starting from an experimental basis, we will motivate why the classical theory of probability is not able to model certain real physical systems. We will present a generalization of the concept of probability that allows us to model these experiments, as well as their (unexpected) consequences. Among the applications in communications are quantum cryptography, the use of quantum entanglement and the teleportation protocol. We will study the underlying principles of quantum computers and we will learn to program them exploiting the quantum parallelism. Finally, the current state and the future perspectives of quantum technology will be discussed.

Some of the course objectives are to:

  • Understand the fundamental differences between classical and quantum probability theories.

  • Describe mathematically a quantum state of a single qubit and that of several qubits.

  • Know and use the axioms that govern the evolution and measurement of a quantum state.

  • Model and analyze simple quantum communication channels and their cryptographic guarantees.

  • Implement and analyze a quantum computing algorithm.

Program

Unit 1. Introduction

  • Historical remarks

  • The polarization of a photon

Unit 2. Axioms of quantum mechanics

  • Binary quantum states and superposition

  • Combining systems: quantum entanglement

  • Evolution of a quantum system

  • Experimental verification: Bell's inequality

Unit 3. Quantum communications

  • Classical and quantum information

  • Modeling quantum channels

  • Communication protocols: teleportation

  • Quantum cryptography

Unit 4. Quantum computing

  • Quantum computers and their programming paradigm

  • Quantum computing algorithms

  • Programming a quantum computer

  • Perspectives and future

Course material