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## Introduction to Quantum Information Theory—PHYS 7895

This course introduces the subject of communication with quantum systems. Quantum information theory exploded in 1994 when Peter Shor published his algorithm that can break RSA encryption codes. Since then, physicists, mathematicians, and engineers have been determining the ultimate capabilities for quantum computation and quantum communication. In this course, we study the transmission of information over a noisy quantum communication channel. In particular, you will learn about quantum mechanics, entanglement, teleportation, entropy measures, and various capacity theorems involving classical bits, qubits, and entangled bits.

Course SyllabusTextbook: Quantum Information Theory (please use this version)

Office Hours: Monday 1:30pm-2:30pm and Thursday 11am-12pm in Nicholson 447

**Scribing.** You are required to scribe two or more lectures, depending on the class size.

### Homeworks

### Lectures

Lecture 27: trade-off coding

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Lecture 26: family of quantum protocols

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Lecture 25: entanglement-assisted classical communication

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Lecture 24: classical communication (cntd.)

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Lecture 23: classical communication

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Lecture 22: entanglement concentration

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Lecture 21: quantum data compression

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Lecture 20: quantum relative entropy, monotonicity, and recoverability

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Lecture 19: quantum relative entropy and quantum entropy inequalities

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Lecture 18: quantum entropies

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Lecture 17: classical entropies and entropy inequalities

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Lecture 16: fidelity and trace distance, gentle measurement

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Lecture 15: trace distance and fidelity

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Lecture 14: trace distance and its operational interpretation

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Lecture 13: isometric extension of a quantum channel

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Lecture 12: coherent communication and purification

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Lecture 11: entanglement distribution, super-dense coding, and teleportation

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Lecture 10: combining channels, adjoints, interpretations of channels, and preparations and measurements as channels

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Lecture 9: reasonable axioms for quantum physical evolutions and the Choi-Kraus theorem

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Lecture 8: more general measurements, POVM formalism, product states, separable states, partial trace operation

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Lecture 7: Schmidt decomposition, density operators, unitary evolution of density operators, measurement in the noisy quantum theory

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Lecture 6: CHSH game, Bell's theorem, and Tsirelson's bound

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Lecture 5: noiseless quantum theory and no-cloning theorem

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Lecture 4: conditional typicality and a proof of Shannon's channel coding theorem

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Lecture 3: repetition code and proof sketch for Shannon's channel coding theorem

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Lecture 2: Huffman code, surprisal, entropy, Shannon data compression

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Lecture 1: introduction to course and discussion of final projects

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Previous course on quantum information theory taught at Louisiana State University Previous course on quantum information theory taught at McGill University

*Last modified: December 22, 2015.*