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The final assignment is a 30-minutes presentation on a research paper related to the lecture. Here are suggested topics:

* Estimate `\tilde\alpha(S) \ge d^2` from R. Duan, Super-activation of zero-error capacity of noisy quantum channels.
* Classification of quantum graphs on M_2 from J. Matsuda, Classification of Quantum Graphs on $M_2$ and their Quantum Automorphism Groups.
* Monotonicity of quantum Lov¨¢sz number from D. Stahlke, Quantum Zero-Error Source-Channel Coding and Non-Commutative Graph Theory. (mainly Section V)
* Compare the convention of quantum homomorphisms / isomorphisms with B. Busto, D. Reutter, D. Verdon, A compositional approach to quantum functions.
* State-sum model behind quantum automorphism of quantum graphs: T. Banica, Quantum automorphism groups of homogeneous graphs.

Assignment due: 20 April

Format: PDF upload on Canvas

Style guide for typing up the lecture notes for mandatory assignment: PDF

We shift the Tuesday lectures to start from 12:45, and end at 14:30. The Friday lectures are unchanged.

The topic for this year is quantum graphs and associated quantum channels. The idea of quantum graphs came out of the paradigm of noncommutative spaces (regard noncommutative algebras as function spaces on ¡®noncommutative spaces¡¯) and operator spaces (subspaces of operators on Hilbert spaces). Our main reference is a recent survey [1] by M. Daws. We supplement it with some research articles (see the syllabus page) from quantum information theory to understand its application to QIT.

1. Matthew Daws. 2022. ¡°Quantum graphs: different perspectives, homomorphisms and quantum automorphisms.¡± (arXiv:2203.08716)