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Quantum Information Theory—PHYS 7347
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: Principles of Quantum Communication Theory: A Modern Approach (please use this version)
Office Hours: Mondays from 4-5pm in Nicholson 447
Homeworks
Homeworks are due by 4pm on Wednesday Sept. 15 (Hwk 1), Sept. 29 (Hwk 2), Oct. 13 (Hwk 3), Oct. 27 (Hwk 4)
Lectures
YouTube video playlist of all lecturesLecture 29: entanglement distillation PDF
Lecture 28: private communication PDF
Lecture 27: classical communication PDF
Lecture 26: entanglement-assisted classical communication, achievability part PDF
Lecture 25: entanglement-assisted classical communication, converse part PDF
Lecture 24: squashed entanglement PDF
Lecture 23: introduction to entanglement theory PDF
Lecture 22: quantum data compression PDF
Lecture 21: Petz--Renyi relative entropy and its properties, monotonicity in alpha and data processing inequality PDF
Lecture 20: generalized divergence, Petz--Renyi relative entropy and its properties PDF
Lecture 19: quantum entropies and information PDF
Lecture 18: fidelity, Uhlmann's theorem, data processing inequality PDF
Lecture 17: quantum Stein's lemma PDF
Lecture 16: quantum Chernoff bound PDF
Lecture 15: hypothesis testing, symmetric and asymmetric settings PDF
Lecture 14: Bell inequality and CHSH game, Tsirelson's bound PDF
Lecture 13: quantum teleportation PDF
Lecture 12: Stinespring dilation theorem (isometric extension of channels), examples of channels: amplitude damping, erasure, Pauli, preparation, appending, replacer, partial trace, unitary, isometric PDF
Lecture 11: quantum channels, Kraus representation, Choi representation, completely positive and trace preserving conditions PDF
Lecture 10: ensembles and classical-quantum states, partial transpose, measurements in quantum mechanics PDF
Lecture 9: qudit Bell states, state purification, group-invariant states PDF
Lecture 8: axioms of quantum mechanics, Bloch sphere, bipartite states, partial trace, separable and entangled states PDF
Lecture 7: mathematical preliminaries: complementary slackness, example of SDP - calculating the spectral norm PDF | CVX Matlab example
Lecture 6: mathematical preliminaries: analysis, convexity, and semi-definite programming PDF
Lecture 5: mathematical preliminaries: functions of Hermitian operators, operator convex, concave, monotone functions, norms, Schatten norm, operator Jensen inequality, superoperators PDF
Lecture 4: mathematical preliminaries: finite-dimensional Hilbert spaces and linear operators PDF
Lecture 3: proof sketch for Shannon's channel coding theorem PDF
Lecture 2: Shannon data compression, repetition code with majority vote decoder PDF
Lecture 1: introduction to course, discussion of final projects, introduction to information theory and Shannon's data compression theorem PDF
Previous 2017 course on quantum information theory taught at Louisiana State University Previous 2015 course on quantum information theory taught at Louisiana State University Previous 2013 course on quantum information theory taught at Louisiana State University Previous course on quantum information theory taught at McGill University
Last modified: January 30, 2022.
