Here are PostScript files for the overhead transparencies that I am using in my lecture series at the University of Innsbruck. At present, they are only available in large format, one A4 slide per page. The lectures were 90 minutes long and average about 20-25 transparencies.
This lecture roots our subject in the "Physics of information" and gives a quick review of classical information theory. Connected to this lecture is this cartoon of Alice and Bob communicating via a physical means. (Lecture given 28 May 1998)
Lecture 2 -- States and Dynamics
This lecture reviews quantum mechanics to establish my notation and gives a brief introduction to density operators and generalized (open system) time evolution. I also give a proof of the representation theorem for trace-preserving completely positive linear maps. I wind up talking about the no-cloning theorem, and I give a precis of the doctrines of the Church of the Larger Hilbert Space. (Lecture given 29 May 1998)
Lecture 3 -- Entropy and Fidelity
I discuss the quantum (von Neumann) entropy is introduced and some of its properties -- especially my favorite properties of strong subadditivity and the existence of "typical subspaces". I then discuss the measure of quantum fidelity and prove that quantum data compression can be done with about S qubits. (Lecture given 2 June 1998)
Lecture 4 -- Classical Information via Quantum Channels
I discuss the problem of sending classical messages using quantum communication channels, and introduce the measure of distinguishability c. I prove a "data processing" inequality for distinguishability; Holevo's theorem follows as a corollary given a physical model of measurement. We can also send up to c bits per letter by appropriate coding and decoding; the proof (for pure states) is given, with the machinery of typical subspaces, random codes, and the "pretty good measurement". (Lecture given 4 June 1998)
Lecture 5 -- Noisy Quantum Channels
First I discuss classical information in noisy channels, finishing the things we did last time. Next we discuss the problem of sending entanglement through a noisy quantum channel. The entanglement fidelity and the entropy exchange are introduced, and are related to one another via the quantum Fano inequality. I also have a graph of the quantum Fano bound for one qubit. (Lecture given 9 June 1998)
Lecture 6 -- Coherent Information,
We introduce the notion of coherent information, and prove the quantum data processing inequality. Perfect quantum error correction is possible if and only if no coherent information is lost in the channel. This suggests that coherent information is related to the quantum channel capacity, but there are curious problems involving quantum supercapacity. Also included are two diagrams (1 and 2) of outlining Lloyd's argument that up to I qubits of entanglement can be sent through a noisy quantum channel with fidelity approaching unity. (Lecture given 10 June 1998)
Lecture 7 -- Some Applications
I discuss three applications of the ideas developed in lectures 1-6: approximate quantum cloning, privacy in quantum cryptography, and the relation of decoherence to the loss of coherent information in a quantum system. (Lecture given 12 June 1998)
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