Ohiko deialdia: orientazioak eta uko egitea

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Irakasgai-zerrenda

Fundamentals

Introduction (Chap. 1 of Gerry-Knight, 4 h). Scope and aim of the course: Quantum Optics as a generic vehicle for quantum information and technologies. History.

Field quantization (Chap. 2 of Gerry-Knight, 8 h). Quantization of a single-mode field. Quantum fluctuations of a single-mode field. Quadrature operators for a single-mode field. Multimode fields. Thermal fields. Vacuum fluctuations and the zero-point energy. The quantum phase.

Coherent states (Chapter 3 of Gerry-Knight, 8 h). Eigenstates of the annihilation operator and minimum uncertainty states. Displaced vacuum states. Wave packets and time evolution. Generation of coherent states. More on the properties of coherent states. Phase-space pictures of coherent states. Density operators and phase-space probability distributions. Characteristic functions.

Light-Matter interaction (Chapter 4 of Gerry-Knight, 3 h). Atom–field interactions. Interaction of an atom with a classical field. Interaction of an atom with a quantized field. The quantum Rabi model; the Jaynes–Cummings model. The Jaynes–Cummings model with large detuning: a dispersive interaction.

Gaussian quantum states and simplectic notation (Serafini, 2 h). Introduction : continuous vs. discrete variables. Definition of continuous-variable quantum state; phase space; Wigner function and quantumness; Gaussian quantum states: Wigner and Characteristic Functions; Bi-linear Hamiltonians; Williamson Theorem; Single- and Two-Mode Quantum States; Negativity and Purity; Gaussian Measurements



Applications

Quantum metrology (Kok-Lovett, 5 h)

From Classical to Quantum Fisher Information: the Continuous-Variable Case; Quantum Fisher Information for Gaussian States; Quantum parameter estimation and hypothesis testing; Entanglement-Assisted Parameter Estimation; Hypothesis Testing; Example: Quantum Illumination; Heisenberg-Limit Interferometry

Quantum computation (Kok-Lovett, 6 h)

Fundamentals of quantum computation: From Boolean functions to Unitaries: Reversible Computation; The Circuit Model: Qubits & Basic Operations; Classical Theorems on Quantum Computation; Measurements: Single-Shot vs. Mean-Values. Quantum Computation in Quantum Optics: the single-photon case; Limitations of Quantum Optics for Quantum Computing: N-port Interferometers; Qubit Codification and Basic Operations: Knill-Lafflame-Milburn Protocol; Post-Selection and Probabilistic Gates. Quantum Computation in Quantum Optics: continuous variables; Quantum States: Squeezed States; Single-Mode Gates; Entanglement: Two-Mode Operations; The Gottesman-Knill Theorem for Continuous Variables

Quantum communications (Kok-Lovett, 4 h)

Remote state preparation and quantum teleportation; Quantum Teleportation: From Qubits to Continuous-Variables; Improvements: Entanglement Swapping and Distillation; Remote State Preparation: From Qubits to Continuous-Variables. Quantum Cryptography: Quantum Key Distribution with Continuous Variables

Bibliografia

Oinarrizko bibliografia

- Introductory Quantum Optics by Gerry and Knight (Cambridge), Chapters 1, 2, 3, 4, 8, and 10.

- Quantum Continuous Variables by Alessio Serafini (Taylor and Francis)

- Introduction to Optical Quantum Information Processing by Pieter Kok and Brendan W. Lovett (Cambridge)

- Additional material is provided via Egela (other books, articles, news, and auxiliary notes for specific topics).