Physics 572 Spring 2019

Quantum Information Theory

 

Instructor: Prof. Elizabeth Crosson

Office: Physics and Astronomy Room 13

Email: crosson@unm.edu

Office Hours: Tuesday 1:00-3:00, Friday 10:00-12:00, room 13

Lectures: Tuesday and Thursday 11:00-12:15, Physics and Astronomy room 5

Online Texts (Optional):

“Lectures notes on Quantum Information and Computation” J. Preskill
“From Classical to Quantum Shannon Theory”, M. Wilde
“Quantum Information Meets Quantum Matter”, B. Zeng, X. Chen, D.L. Zhou, X.G. Wen

Grading:
• Problem Sets: 80%
• Class Participation: 20%

PDF Syllabus

Schedule of Topics


Part 1: Quantum Information Processing
Axiomatic Quantum Mechanics
Probability and Statistics
Mixed States and Quantum Operations
Classical Information Theory
Entanglement Measures and Local Operations
Bell’s Inequality and Hidden Variable Theories
Quantum Communication and Cryptography


Part 2: Quantum Physics and Complexity
Quantum Many-Body Physics
Local Hamiltonians and Quantum Computation
Phases of Quantum Matter
Entanglement in Quantum Ground States
Classical and Quantum Computational Complexity
The Local Hamiltonian Problem
Classical Simulations of Quantum Systems
Sampling Complexity and Quantum Supremacy

Lecture Notes


Date

 Topic

 Notes

Jan. 22

 Mathematical Models in Theoretical Physics,
Classical Probability Theory and Linear Algebra

Slides 1

 Jan. 24

Generalized Probability Theory,
Axioms of Quantum Mechanics

Slides 2

 Jan. 29

Physical Content and Hamiltonians,
Qubits: Observables and Operations

Slides 3

 Jan. 31

Amplitudes vs Mixtures, Incompatible Measurements,
Introduction to Entanglement

Slides 4

 Feb. 5

Entangling Hamiltonians, Quantum subsystems
density matrices, partial trace, Schmidt decomposition

Slides 5

 Feb. 7

Quantum Channels: Krauss operator-sum representation,
depolarizing, dephasing, amplitude-dampening channels

Slides 6

 Feb. 14

Classical Information Theory
Shannon entropy, relative entropy, mutual information
Shannon's paper , Witten's notes

Slides 7

 Feb. 19

Homework 1: entanglement and correlations, distance between quantum states, quantum channels, capacity and mutual information. Due Date: March 7th, 2019.

Problem Set

 Feb. 21

convex functions, data processing inequalities, correlation functions, von Neumman entropy, quantum mutual information, measurements and entropy

Slides 8