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Lecturer(s)
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Marek Petr, prof. Mgr. Ph.D.
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Course content
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1. Quantization of electromagnetic field, continuous variables of electromagnetic field, light as quantum oscillator, Fock states of quantum oscillator, commutation relations, operator algebra. Representations of quantum mechanics. 2. Gaussian quantum states and their description, variance matrix. Gaussian operations and Gaussian measurements. Dynamics of Gaussian systems. 3. Quantum entanglement. Criteria, measures, and witnesses of quantum entanglement. Partial transposition, Simon and Duan criteria. Generating quantum entanglement. 4. Quantum teleportation, deterministic and conditional. Measurement induced quantum operations. Quantum decoherence. 5. No-go theorem on distillation of Gaussian entanglement by Gaussian operations. Non-Gaussian operations in quantum optics. Non-Gaussian quantum states and methods of their generation. 6. Quantum cloning of continuous variables. Conditional and non-conditional amplification of quantum states and their use in contemporary experiments. 7. Information in quantum continuous variables. Quantum key distribution (QKD) with continuous variables, optimal attack, effect of decoherence on QKD. 8. Universal quantum computation with continuous variables. Cubic nonlinearity, its properties and methods of realization. Measurement quantum computation, cluster states, Gottesman-Kitaev-Preskill (GKP) states.
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Learning activities and teaching methods
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Lecture, Monologic Lecture(Interpretation, Training), Dialogic Lecture (Discussion, Dialog, Brainstorming), 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
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Learning outcomes
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The aim of the course is to obtain the theoretical knowledge about quantum systems with continuous variables (CV) and the elementary protocols for CV quantum information processing.
Application of knowledge. Understanding of elementary protocols in quantum information processing with continuous variables and the ability to describe them theoretically and simulate numerically.
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Prerequisites
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OPT/KK1
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Assessment methods and criteria
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Oral exam
Attendance in lectures is voluntary, but strongly recommended. Students are expected to study relevant papers ahead of the class. The passing credit is awarded by completing a homework assignement and defending it during the oral exam.
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Recommended literature
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Cerf, N. J., Leuchs, G., & Polzik, E. S. (2007). Quantum information with continuous variables of atoms and light. London.
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Furusawa, A., & Loock, P. (2011). Quantum teleportation and entanglement: a hybrid approach to optical quantum information processing. Weinheim.
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Gerry, C. C., & Knight, P. L. (2005). Introductory quantum optics. Cambridge.
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Leonhardt, U. (2010). Essential Quantum Optics. Cambridge.
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