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Course: Quantum Commun. & Info Processing 2

Department/Abbreviation: OPT/KKZI2

Year: 2021

Guarantee: 'doc. Mgr. Petr Marek, Ph.D.'

Annotation: 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.

Course review:
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 non-Gaussian measurements. Conditional operations on Gaussian states. 8. No-go theorems about quantum distillation of entanglement. Non-Gaussian 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.