Time:  MWF 12:00-12:50pm 

https://illinois.zoom.us/j/83227321296?pwd=NS9lOEdSWjNxN2FXUm5EQzFvT0h6Zz09

Location:  Virtual

Recordings:

Instructor: Marius Junge    

O: Introduction 

I)   Classical Gates:  What is gate classical gate, and how many functions can we compute with  limited resources?

II)  Classical Information Theory: How can information be send with a noisy device. A first glance at Shannon's model of noisy channels, and the background we need from probability. In particular, we will discuss joint distributions and independence.       

III) Normed spaces and linear maps:  Basic definitions and examples, norm of linear maps, convex sets and extreme points.

IV) Hilbert spaces, unitaries and densities:  We discuss differen norms on the space of matrices and positive definite matrices.   

V)  Quantum gates,  measurements, entanglement, purification and fidelity. 

VI)  Entropy, classical and quantum,  mutual information, equiparititon theorem.

VII) Quantum channels, Stinespring theorem, complementary channel,  Data processing inequality. 

VIII) Capacity (with entanglement)

IX)  Qauntum devices beating classical ones. 

For Notes: See Box 

Books:  (We will mostly follow Wilde's book) 

Michael A. Nielsen & Isaac L. Chuang:  Quantum Computation and Quantum Information, Cambridge University Press 2010.

Mark Wilde:  From Classical to Quantum Shannon Theory, Cambridge University Press, 2013.

John Preskill:  Quantum Computation , lectures notes from CalTech

John Watrous: The Theory of Quantum Information , Cambridge University press 2018.

G. J.A. Jameson: Summing and nuclear norms in Banach spaces, Cambridge University press, 2009 

G. Pisier: Factorization of Linear Operator and geometry of Banach Spaces, AMS series no 60 

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