Quantum Information (WS 20/21)

Lecturers:
Prof. Dr. J. Ignacio Cirac (Max-Planck-Institute of Quantum Optics)
Prof. Dr. Michael M. Wolf (TUM Department of Mathematics)

Overview

The course, which is part of the Master’s Program Quantum Science & Technology, will be entirely online. Lecture videos will be posted here every Tuesday and Thursday at 14:15, starting on Nov. 3rd 2020. Exercises will take place every Wednesday online at 14:00 starting on Nov. 4th 2020.

Content

Quantum Information offers an introduction to the theoretical foundations of Quantum Science and Technology. The course starts with a brief motivation and an introduction to fundamental concepts and the basic formalism (pure/mixed states, evolution, completely positive maps, measurements Schmidt decomposition, tomography, quantum estimation, hypothesis testing). Then the concept of entanglement is discussed in detail, including the distinction between pure and mixed-state entanglement, entanglement entropy, quantification and conversion. Subsequently, some of the revolutionary promises of exploiting entanglement are presented, including dense coding, quantum teleportation and quantum cryptography. Next the Bell inequalities, characterizing the quantum weirdness of entanglement and non-locality, are introduced and discussed in detail. Subsequent chapters cover central applications of quantum information theory: quantum computation, quantum algorithms such as those of Deutsch, Shor and Grover, and quantum simulation. Final core topics are decoherence, Lindbladian descriptions thereof, and error correction schemes to counteract the consequences of decoherence and protect fragile quantum information. The module will typically also include one or more optional topics, such as many-body entanglement, topological quantum computation, quantum complexity, or tensor networks, which link quantum information theory to many-body physics.

General Literature

Standard articles, textbooks, and lecture notes on Quantum Information are:

Quantum Computing Pfeil, an article by J.Eisert and M.M.Wolf.
Quantum Computation Pfeil (Lecture Notes), John Preskill. A famous set of lecture notes, continually being refined throughout the last 20 years.
Quantum Computation and Quantum Information Pfeil, 10th Anniversary Edition, Michael A. Nielsen, Isaac L. Chuang, Cambridge University Press, 2010. One of the most cited books in physics of all time, providing a general, accessible and wide-ranging introduction to the topic.

Material

Date	Content
Nov 4th	Chapter 0: Linear Algebra for Q. Information
Nov 3rd	Chapter 1: Basic Concepts in Q. Information Part 1: Single systems: Introduction, States
Nov 5th	Chapter 1: Basic Concepts in Q. Information Part 1 (cont): States, Observables & Measurements
Nov 10th	Chapter 1: Basic Concepts in Q. Information Part 1 (cont): Evolution, General Dynamics, Part 2: Composite Systems: Introduction, States
Nov 12th	Chapter 1: Basic Concepts in Q. Information Part 2 (cont): States, Observables & Measurements
Nov 17th	Chapter 1: Basic Concepts in Q. Information Part 2 (cont): Evolution, General Dynamics
Nov 19th	Chapter 2: Entanglement and non-locality: EPR "paradox", Bell's theorem, CHSH inequalities
Nov 24th	Chapter 2: Entanglement and non-locality: Bell's theorem without inequalitites, Noncontextuality, Causality
Nov 26th	Chapter 3: Quantum Communication: Part 1: Cryptography: Classical Cryptograph, Quantum Key Distribution
Dec 1st	Chapter 3: Quantum Communication: Part 1 (cont): Eavesdropping
Dec 3rd	Chapter 3: Quantum Communication: Part 2: Complexity: Classical, Quantum
Dec 8th	Chapter 3: Quantum Communication: Part 3: Repeaters: Imperfections, Basic concepts
Dec 10th	Chapter 3: Quantum Communication: Part 3: Repeaters (cont): Entanglement distillation, Repeaters
Dec 15th	Chapter 4: Quantum Computing: Part 1: Basics: Classical computing, Quantum computing basics
Dec 17th	Chapter 4: Quantum Computing: Part 1: Basics (cont): Quantum circuits, Complexity
Dec 22nd	Chapter 4: Quantum Computing: Part 2: Quantum algorithms: with and without oracles
Jan 7th	Chater 4: Part 2: Quantum algorithms: Phase estimation, amplitude amplificatin, quantum simulation
Jan 12th	Chater 4: Part 2: Quantum algorithms: Adiabatic, variational, other computational models
Jan 14th	Chater 4: Part 3: Quantum error correction: Classical, simple QEC: flips and phases, general QEC
Jan 18th	Chater 4: Part 3: Quantum error correction: Stabilizer Codes, Fault-tolerant error correction
Jan 20th	Chater 5: Quantum metrology: Atomic clocks, Fisher Information, Quantum Fisher Information, Cramer-Rao bounds
Jan 26th	POVMs: axiomatic & operational description, Naimark's theorem, applications in (unambiguous) state discrimination and information transmission
Jan 29th	Quantum channels: tpcp maps, Choi-Jamiolkowski matrix, Kraus representation, environment representation, dephasing/entanglement breaking channels
Feb 2nd	Entanglement: correlations, separability, witnesses, positive map criteria, DeFinetti characterization, basic entanglement measures & their relations, bound entanglement
Feb 4th	Period finding: Simon's algorithm, collision problem, Shor's algorithm, hidden subgroup problems
Feb 9th	Chapter 6: Physical implementations: Photons
Feb 11th	Chapter 6: Physical implementations: Trapped ions

More Material (e.g. Videos of the lectures) can be found on Moodle.