Introduction to quantum information theory

- Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava (3 credits)
- subject code 1-FYZ-402, summer semester
- bachelor and master students
- lecturers: Mário Ziman
- summer semester 2015, Tuesdays 13:10-14:40, room F2-225

Content: (updated for summer semester 2015)
§ 1. Quantum key distribution
    - polarization, one-time pad, protocol B92
§ 2. Qubit
    - quantum information, qubit, Pauli operators, Bloch sphere, density operators, quantum NOT gate, logical NOT gate,
§ 3. Two qubits
    - entanglement, no-signalling, no-cloning,
§ 4. EPR paradox a Bell inequalities
    - locality and reality, EPR reasoning, CHSH inequalities, violation,
§ 5. Quantum teleportation and superdense coding
    - entanglement, Bell basis and measurement, super-dense coding, teleportation
§ 6. Quantum gates and algorithms
    - interferometers, √NOT gate, elementary gates, Deutch-Jozsa algorithm,
§ 7. Grover's database search algorithm
    
§ 8. Shor's algorithm
    - RSA cryptosystem, factorisation problem, inverse logarithm, Fourier transformation,
§ 9. Physical implementations of qubits
    - di Vincenzo criteria, photons, trapped ions, quantum dots, charge qubits, decoherence
§ 10. Quantum compression
    
§ 11. Quantum walks
    

Homeworks:
1. Consider someone sends you photons using one of the following two procedures:
(A) randomly preparing horizontal or vertical polarization; or
(B) randomly preparing left-circular, or right-circular polarization.
If possible, suggest an experiment able to discriminate which procedure was used.
2. How to measure an unknown state produced by a source of qubits? (for example the state of photon's polarization?) If possible, propose some experimental procedure.