Lecturer(s)


Filip Radim, prof. Mgr. Ph.D.

Course content

1. Mathematical principles of quantum mechanics: complex Hilbert space, orthonormal vectors, operator properties and operator representations, tensor product of Hilbert spaces, projector properties, completely positive maps. 2. Physical principles of quantum mechanics: quantum mechanics postulates, quantum interference, violation of local realism of classical theory, evolution of quantum systems, quantum channels, measurement in quantum mechanics. 3. Quantum information: quantum bit, quantum analog signal, quantum state discrimination, quantum cloning, quantum entanglement, measure of quantum entanglement. 4. Quantum channels, classical and quantum capacity of quantum channel, quantum codes. 5. Principles of quantum cryptography: protokol BennetBrassard (BB84), protocol Bennet (B92), protocol based on entangled states. 6. Conditional and unconditional security of quantum cryptography, quantum repeaters, optimal individual and collective attacks, unconditional security, robustness of quantum cryptography. 7. Experimental implementation of quantum cryptography: protocols with single photons, coherent states, quantum memories, experimental realization of quantum repeaters. 8. Recent problems of quantum cryptography. 9. Quantum cryptography with many users: quantum entanglement between many users, GHZ a W quantum states, quantum secret sharing.

Learning activities and teaching methods

Dialogic Lecture (Discussion, Dialog, Brainstorming)
 Homework for Teaching
 80 hours per semester
 Attendace
 20 hours per semester

Learning outcomes

This course shows a basic survey of using principles of quantum mechanics in secure publickey distribution. The aim of course is to understand basic principles of quantum information, physical methods and experimental implementations of quantum cryptography and also learn about recent problems in this field. Attending students could obtain a practical skill in application of quantum mechanics in information transmission.
1. Knowledge Describe and understand comprehensively principles and methods of quantum cryptogtaphy.

Prerequisites

unspecified

Assessment methods and criteria

Oral exam
In the scope of the course.

Recommended literature


Alber G., Beth T., Horodecki M., Horodecki P., Rötteler M., Weinfurter H., Werner R. F., Zeilinger A. (2001). Quantum Information. Springer Tracks in Modern Physics.

Bouwmeester D., Ekert A., Zeilinger A. (2000). The Physics of Quantum Information. SprigerVerlag.

Formánek J. (2004). Úvod do kvantové teorie, část I. Academia, Praha.

Formánek J. (2004). Úvod do kvantové teorie, část II. Academia, Praha.

Gisin N., Ribordy G., Tittel W. and Zbinden H. (2002). Quantum cryptography. Rev. Mod. Phys. 74, 145195.

Lo H.K., Spiller T., Popescu S. (1999). Introduction to Quantum Computation and Information. World Scientific Publishing Company.

Nielsen M. A., Chuang, I. L. (2004). Quantum Computation and Quantum Information. Cambridge University Press.

Peres A. (1996). Quantum Theory: Concepts and Methods. Kluwer, Dordrecht.
