Lecturer(s)


Park Kimin, Ph.D.

Filip Radim, prof. Mgr. Ph.D.

Marek Petr, Mgr. Ph.D.

Course content

1. Quantization of electromagnetic field, continuous variables of electromagnetic field, light as quantum oscillator, Fock states of quantum oscillator, commutation relations, operator algebra. Pictures of quantum mechanics. 2. Basic Gaussian quantum states, Gaussian operations and Gaussian measurements in Heisenberg picture. 3. Quantum cloning of continuous variables. Amplification of quantum states. Reversibility of cloning. Probabilistic cloning. 4. Quantum entanglement of Gaussian states, its generation, detection and properties, Duan and Simon criteria, measure of entanglement, conditional preparation of quantum state. 5. Quantum teleportation and measurement induced operations. Quantum decoherence and its influence on quantum entanglement and quantum operations. 6. Information in quantum continuous variables. Quantum key distribution (QKD) with continuous variables, optimal attack, effect of decoherence on QKD. 7. Covariance matrix of Gaussian state. Extremality of Gaussian states. Security of QKD against collective attacks. Wigner function, Gaussian operations with Wigner function, Gaussian and nonGaussian measurements. Conditional operations on Gaussian states. 8. Nogo theorems about quantum distillation of entanglement. NonGaussian states and their distillations. Distillation of entanglement by photon subtraction, advantage/disadvantage. Hybrid quantum information processing. 9. Universal quantum computing with continuous variables, cubic interaction, preparation and properties. Quantum cluster states with continuous variables.

Learning activities and teaching methods

Lecture, Work with Text (with Book, Textbook)
 Homework for Teaching
 26 hours per semester
 Preparation for the Course Credit
 13 hours per semester
 Attendace
 39 hours per semester

Learning outcomes

The aim of the course is to obtain the theoretical knowledge about quantum systems with continuous variables and also learn about their basic experimental tests.
Application of knowledge. Show an ability to apply knowledge and principles for a solution of particular problems in the concrete situations.

Prerequisites

OPT/KK1

Assessment methods and criteria

Oral exam
<ul> <li> Active attendance in the exercise classes </ul>

Recommended literature


Cerf, N. J., Leuchs, G., & Polzik, E. S. (2007). Quantum information with continuous variables of atoms and light. London: Imperial College Press.

Furusawa, A., & Loock, P. (2011). Quantum teleportation and entanglement: a hybrid approach to optical quantum information processing. Weinheim: WileyVCH.

Gerry, C. C., & Knight, P. L. (2005). Introductory quantum optics. Cambridge: Cambridge University Press.
