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. The new quantum theory of probability will then be used to analyze several simple problems, including the transmission of information, the distribution of quantum entanglement and the teleportation protocol. Finally, the current state of the technology and its future perspectives will be discussed.
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Contents
Unit 1. Introduction: bits versus qubits
1.1. What is a qubit?
1.2. Quantum states
1.3. Experiments and quantum systems
Unit 2. Axioms of quantum mechanics
2.1. Principles of quantum mechanics
2.2. Combining systems: quantum entanglement
2.3. Experimental verification: Bell¿s inequality
2.4. Time and evolution of a system
Unit 3. Quantum communications
3.1. Modeling quantum channels
3.2. Classical versus quantum information
3.3. Communication protocols: polarization and entanglement
3.4. Secure link Alice-Bob-Eve
Unit 4. Quantum computation
4.1. Resources and tasks
4.2. Teleportation
4.3. Protocols: entanglement distribution and super-dense coding
4.4. Quantum computers: state of the art