ECE 498EC: Quantum Information Processing, FA 2021

Course Description – This course introduces the basic concepts and principles underlying quantum computing and quantum communication theory.  Roughly 33% of the course will be devoted to teaching the necessary mathematical tools and principles of quantum information processing, 33% to quantum computation and communication, and 33% to entanglement theory.  The specific topics covered in this course are chosen to reflect areas of high interest within the research community over the past two decades.  The student will be expected to perform detailed mathematical calculations and construct proofs.  By the end of the semester, the student should be equipped with enough background and technical skill set to begin participating in quantum information research.

Format and Schedule –  Live lectures will be given in person T/R 3:00PM – 4:20PM, and these will also be recorded for future viewing.

Prerequisites – Linear algebra required; quantum mechanics, and probability/statistics recommended.

Textbook – The primary course material will be lecture notes generated by the instructor.  A suggested supplemental textbook is Quantum Computation and Quantum Information by M.A. Nielsen and I.L. Chuang.

Grading – Grades will be based on 50% homework, 25% Midterm, and 25% Final.

Four Credit Option – This course can be taken for four credits.  The additional credit requires writing a review paper on some quantum information research article.  The paper should be at least six pages in length and provide a background discussion of the paper, a derivation of the major results, and a conclusion describing future areas of research.  All papers to be reviewed must be pre-approved by the instructor, and suggested papers can also be provided.

Syllabus –

	Lecture	Main Topic	Subtopics
Part I: Fundamental Principles of Quantum Information Processing	1	The State Space Axiom	Bras/kets, density operator
	2		Qubits and Bloch Sphere
	3	Multiple System Axiom	Partial Trace, Reduced Density Operator
	4		Schmidt Decomposition, Two-Qubit Systems
	5	The State Evolution Axiom	Unitary Evolution
	6		Qubit and Multi-qubit gates
	7		Completely-Positive Maps
	8		The Choi Matrix and Qubit Channels
	9	The Quantum Measurement Axiom	Projective Measurements and Superdense Coding
	10		Quantum Observables and Classical Knowledge
	11		Quantum Instruments and POVMs
Part II: No-Go’s and Optimal Approximations	12	Indistinguishable States and No-Cloning	The Quantum State Discrimination Problem
	13	Quantifying Closeness of Quantum States	Trace Distance and Fidelity
	14		Helstrom’s Measurement
	15	Semi-Definite Programming and Optimal State Discrimination	SDP, Duality, and KKT Conditions
	16		Conditions for Min-Error State Discrimination
	17	No-Signaling and Nonlocality	No-Signaling and State Discrimination
	18		Local Hidden Variable Models and Bell Inequalities
	19		The CHSH Inequality
	20		Tsierlen’s Inequality and Nonlocal Boxes
	21		Quantum Steering
Part III: Quantum Communication and Entanglement Theory	22	Quantum Teleportation	Teleportation Protocols, Resource Trade-offs
	23		Teleportation Fidelity, Local Twirling
	24	Entanglement and Separability	Local Operations and Classical Communication (LOCC)
	25		Separability Criterion, PPT Entanglement
	26	Detecting and Measuring Entanglement	Entanglement Witnesses
	27		Entanglement Measures
	28	Asymptotic Entanglement Transformations	Pure-state Entanglement Distillation
	29		Mixed-state Entanglement Distillation
	30		Bound Entanglement