Introduction to quantum information theory

- Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava
- spring semester, 2008-2011
- lecturers: Mário Ziman, Daniel Nagaj

Description:

§ 1. Quantum key distribution
one-time pad, protocol BB84 (Bennett, Brassard), security, no-cloning theorem,

§ 2. Elements of quantum theory
polarization and quantum probabilities, interferometers, quantum superposition, projection postulate, Schroedinger equation

§ 3. Quantum bit
bit of information, quantum encoding, Bloch sphere, pure and mixed states, Pauli operators, purity, von Neumann entropy

§ 4. Two quantum bits
tensor product, pure state entanglement, reduced states, mutual information

§ 5. EPR paradox a Bell inequalities
locality and reality, EPR reasoning, CHSH inequalities, violation, no-signaling principle

§ 6. Teleportation, superdense coding a one-time pad
Bell basis and measurement, one-time pad, superdense coding, teleportation

§ 7. Quantum entanglement
separable states, LOCC operations, Perez-Horodecki criterion,

§ 8. Quantum gates
Deutch-Jozsa algorithm, universality, Groover search algorithm

§ 9. Shor's algorithm
inverse logarithm, Fourier transformation,

§ 10. Physical implementations
di Vincenzo criteria, communication qubits (photons), computational qubits (trapped ions, quantum dots, charge qubits)

Exam:
homeworks (50%), written test (50%) plus oral exam