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Quantum Information Theory, 2014
Course manager: Jan-Åke Larsson
Suggested credits: 6 hp
Course literature
The course will be based on the book Quantum Computation and Quantum Information by Michael A. Nielsen and Isaac L. Chuang, ISBN 9780521635035.
Organisation
Lectures will be given by Jan-Åke, and examination will be by hand-ins.
This time around, the course will as far as is possible be tuned for students with some knowledge of quantum mechanics, but not necessarily with a background in information theory.
After each lecture a number of problems to solve will be given. The problems should be solved individually by each participant, but it’s ok to discuss the problems with each other. You should turn in your solutions no later than a week after they are given.
Lectures
Below is a very preliminary lecture schedule which is to be adapted to this year’s students’ background. Also, most of the topics could fill several lectures. The pace will be adjusted depending on the background and interests of the students.
The first meeting will be in Nollstället on October 30 2014, at 15:15. Later dates will be decided with the participants, say one lecture per week.
| # | Date and time | Subject | Content | Book chapter | Assignments |
|---|---|---|---|---|---|
| 1 | 30/10, 15:15 | Introduction to Quantum Mechanics | Polarized light, light quantum, vector space description, Dirac ket notation. subspaces as events, spin-1/2, the Bloch sphere, projection operators, measurement, the Born rule, Pauli matrices | 1, 2.1.1-2.1.6, 2.2.1-2.2.5 | 2:9, 10, 11, 19, 20, 21 |
| 2 | 13/11, 15:15 | Measurement, mixed states | Measurement operators, joint measurement, joint eigenspaces, commutator, Hermitian operators, state transformations, unitary operators, the Schrödinger equation, mixed state, Trace as scalar product, trace as probability, density operator, proper and improper mixtures, spectral decomposition | 2.1.6, 2.1.8-2.1.9, 2.2.2-2.2.5, 2.4.1-2.4.2 | 2: 35, 37, 39, 47, 57, 58, 71, 72 |
| 3 | 28/11, 15:15 | Composite systems | Composite systems, tensor product, entanglement, pure states, partial trace, separability, teleportation, purification, Schmidt decomposition | 2.1.7, 2.2.8, 2.4.3, 2.5 | 2.67*, 2.74, 2.75, 2.81, 2.82 |
| 4 | 9/12, 15:15 | Quantum entropy | Von Neumann entropy, relative entropy, the Klein inequality, positivity and upper bounds, subadditivity, lower bounds | 11.1-11.2, 11.3.1-11.3.2 | 11.2*, 11.5, 11.7, 11.11, 11.12 |
| 5 | 16/12, 15:15 | Quantum entropy (continued) | Entropy for bipartite systems, conditional entropy, mutual information, Venn diagram, negative conditional entropy, tripartite systems | 11.3.2-11.3.4 | 11.13, 11.14, 11.16 |
| 6 | 13/1, 15:15 | Entropy for mixed states | Entropy for mixtures as mixture of entropies, measurements increase the entropy, Concavity of entropy. | 11.3.3, 11.3.5-11.4 | 11.19, 11.20 |
| 7 | 23/1, 13:15 | Accessible information, Quantum Source coding | The Holevo bound. Strong subadditivity. Lieb's theorem. Convexity of relative entropy. Concavity of conditional entropy. | 11.4,12.1 | 11.24, 11.25, 11.26 |
| 8 | 30/1, 15:15 | Quantum channels | Quantum operations, and connection to generalized quantum measurements, trace-preserving operations, quantum channels, examples | 8 | 8.4, 8.6, 8.10, 8.22, 8.29 |
| 9 | 12/2, 13:15 | Noise measures | Trace distance, fidelity, properties of the fidelity, examples, entanglement fidelity | 9 | |
| 10 | 27/3, 15:15 | Quantum source coding, Quantum error correction, Quantum channel coding | 12,10 | ||
| 11 | Quantum data processing inequality, ... | 12 |