Physics 581.001 Quantum Information Theory Spring 2009

Phys 581.001 Quantum Information Theory Spring 2009

Syllabus

The syllabus provides a schedule for the course and access to all the web-based material. Click on the appropriate document to get a pdf file for lecture notes, special handouts, homework assignments, and solution sets.

I'm pretty confident we can cover the material in the time allotted, but this being the first time I've taught this material in 2/3 of a semester, there are likely to be changes in schedule as we go along. This means you should consult the syllabus often to keep track of changes.

Students adopting the graded track will be graded on their performance on the homework assignments. To receive a grade of CR on the ungraded track, students need only attend the lectures and show interest. There will not be any exams.

Each homework assignment will consist of several problems, some of which will be quite ambitious. The homework assignments scheduled in the syllabus reflect the maximum amount of homework I might assign. I might not get around to making up all the scheduled assignments, although I'm hoping there will be something significant for all the homework assignments.

I want to learn some new things by teaching this course, so during the period when I'm in Australia, students who want to and I will read key papers on two topics: (i) matrix-product states and density-matrix renormalization group; (ii) quantum Shannon theory. Formulating a summary of what we have learned will occupy the last week of classes and perhaps some of finals week.

Homework Class session Lectures Nielsen
and Chuang Preskill

T, 1-20 Brief introduction to course
Adjourn to inaugural party of your choice.

HW #1
(Out 1-22)
Solutions Th, 1-22 L1: Probabilities and laws of large numbers
Probabilities as betting odds and the Dutch book. Simple Dutch-book derivation of the probability rules in a seminar talk.

T, 1-27 L2: Classical information and Shannon entropy 11.1-11.2
12.2.1 5.1

Th, 1-29 L3: Linear algebra and axioms of quantum mechanics 2.1-2.3 2.1

T, 2-3 L4: Qubits 1.2-1.3 2.2, 2.3.2

HW #2
(Out 1-29)
Solutions Th, 2-5 L5: Quantum states. I. Mixed states 2.2-2.6 2, 4.1-4.4

T, 2-10 L6: Quantum states. II. Multiple systems and entanglement
L6-7
Multiple systems, the tensor-product space, and the partial trace

HW #3
(Out 2-5)
Solutions Th, 2-12 L7: Quantum states. III. Multiple systems and entanglement

T, 2-17 L8: Quantum dynamics and measurements. I. Generalized measurements 2.2 3.1

HW #4
(Out 2-19)
Solutions Th, 2-19 No lecture

T, 2-24 L9: Quantum dynamics and measurements. II. Superoperators and completely positive maps 8.1-8.2
8.4-8.5 3.2-3.3
3.5

Th, 2-26 L10: Quantum circuit model 1.2-1.3
4.1-4.4
8.3 3.4

T, 3-3 L11: Quantum circuit model and qubit operations

HW #5
(Out 2-26)
Solutions Th, 3-5 L12: Qubit operations

T, 3-10 L13: Cloning and distinguishability. I
L13-14 9 4.2.3

Th, 3-12 L14: Cloning and distinguishability. II

HW #6
(Out 3-10)
Solutions T, 3-17 Spring Break

Th, 3-19 Spring Break

T, 3-24 L15: Quantum entropy. I
L15-16 11.1-11.4
12.1-12.2 5.1-5.4

Th, 3-26 L16: Quantum entropy. II

T, 3-31 No lecture

HW #7
(Out 3-26)
Solutions Th, 4-2 No lecture

T, 4-7 No lecture

Special topics
I will be away, mainly in Brisbane, from March 27 through May 1. During this period students who want to and I will work on reading papers on the two special topics listed below. Communication will be via Skype (cmcaves) or my SkypeIn number [(505)715-6689], keeping in mind that Brisbane is eight hours behind Albuquerque plus a day.

Matrix-product states and density-matrix renormalization group
1. D. Perez-Garcia, F. Verstraete, M. M. Wolf, and J. I. Cirac, "Matrix product state representations," Quantum Information and Computation 7, 401-430 (2007).
2. U. Schollwöck, "The density-matrix renormalization group," Reviews of Modern Physics 77, 259-315 (2005).
3. G. De Chiara, M. Rizzi, D. Rossini, and S. Montangero, "Density matrix renormalization group for dummies," Journal of Computational and Theoretical Nanoscience 5, 1277-1288 (2008).

Quantum Shannon theory
1. A. W. Harrow, "Coherent communication of classical messages," Physical Review Letters 92, 097902 (2003).
2. I. Devetak, A. W. Harrow, and A. Winter, "A family of quantum protocols," Physical Review Letters 93, 230504 (2004).
3. P. Hayden, D. Leung, P. W. Shor, and A. Winter, "Randomizing quantum states: Constructions and applications," Communications in Mathematical Physics 250, 371-391 (2004).
4. P. Hayden, D. W. Leung, and A. Winter, "Aspects of generic entanglement," Communications in Mathematical Physics 265, 95-117 (2006).
5. A. Abeyesinghe, I. Devetak, P. Hayden, and A. Winter, "The mother of all protocols: Restructuring quantum information's family tree," arXiv:quant-ph/0606225.
6. I. Devetak, A. W. Harrow, and A. J. Winter, "A resource framework for quantum Shannon theory," IEEE Transactions on Information Theory IT--54, 4587-4618 (2008).

T, 5-5 Update on special topics

Th, 5-7 No lecture

Homework	Class session	Lectures	Nielsen and Chuang	Preskill
	T, 1-20	Brief introduction to course Adjourn to inaugural party of your choice.
HW #1 (Out 1-22) Solutions	Th, 1-22	L1: Probabilities and laws of large numbers Probabilities as betting odds and the Dutch book. Simple Dutch-book derivation of the probability rules in a seminar talk.
	T, 1-27	L2: Classical information and Shannon entropy	11.1-11.2 12.2.1	5.1
	Th, 1-29	L3: Linear algebra and axioms of quantum mechanics	2.1-2.3	2.1
	T, 2-3	L4: Qubits	1.2-1.3	2.2, 2.3.2
HW #2 (Out 1-29) Solutions	Th, 2-5	L5: Quantum states. I. Mixed states	2.2-2.6	2, 4.1-4.4
HW #2 (Out 1-29) Solutions	T, 2-10	L6: Quantum states. II. Multiple systems and entanglement L6-7 Multiple systems, the tensor-product space, and the partial trace
HW #3 (Out 2-5) Solutions	Th, 2-12	L7: Quantum states. III. Multiple systems and entanglement
HW #3 (Out 2-5) Solutions	T, 2-17	L8: Quantum dynamics and measurements. I. Generalized measurements	2.2	3.1
HW #4 (Out 2-19) Solutions	Th, 2-19	No lecture
	T, 2-24	L9: Quantum dynamics and measurements. II. Superoperators and completely positive maps	8.1-8.2 8.4-8.5	3.2-3.3 3.5
	Th, 2-26	L10: Quantum circuit model	1.2-1.3 4.1-4.4 8.3	3.4
	T, 3-3	L11: Quantum circuit model and qubit operations
HW #5 (Out 2-26) Solutions	Th, 3-5	L12: Qubit operations
	T, 3-10	L13: Cloning and distinguishability. I L13-14	9	4.2.3
	Th, 3-12	L14: Cloning and distinguishability. II	9	4.2.3
HW #6 (Out 3-10) Solutions	T, 3-17	Spring Break
	Th, 3-19	Spring Break
	T, 3-24	L15: Quantum entropy. I L15-16	11.1-11.4 12.1-12.2	5.1-5.4
	Th, 3-26	L16: Quantum entropy. II	11.1-11.4 12.1-12.2	5.1-5.4
	T, 3-31	No lecture
HW #7 (Out 3-26) Solutions	Th, 4-2	No lecture
HW #7 (Out 3-26) Solutions	T, 4-7	No lecture
Special topics I will be away, mainly in Brisbane, from March 27 through May 1. During this period students who want to and I will work on reading papers on the two special topics listed below. Communication will be via Skype (cmcaves) or my SkypeIn number [(505)715-6689], keeping in mind that Brisbane is eight hours behind Albuquerque plus a day. Matrix-product states and density-matrix renormalization group 1. D. Perez-Garcia, F. Verstraete, M. M. Wolf, and J. I. Cirac, "Matrix product state representations," Quantum Information and Computation 7, 401-430 (2007). 2. U. Schollwöck, "The density-matrix renormalization group," Reviews of Modern Physics 77, 259-315 (2005). 3. G. De Chiara, M. Rizzi, D. Rossini, and S. Montangero, "Density matrix renormalization group for dummies," Journal of Computational and Theoretical Nanoscience 5, 1277-1288 (2008). Quantum Shannon theory 1. A. W. Harrow, "Coherent communication of classical messages," Physical Review Letters 92, 097902 (2003). 2. I. Devetak, A. W. Harrow, and A. Winter, "A family of quantum protocols," Physical Review Letters 93, 230504 (2004). 3. P. Hayden, D. Leung, P. W. Shor, and A. Winter, "Randomizing quantum states: Constructions and applications," Communications in Mathematical Physics 250, 371-391 (2004). 4. P. Hayden, D. W. Leung, and A. Winter, "Aspects of generic entanglement," Communications in Mathematical Physics 265, 95-117 (2006). 5. A. Abeyesinghe, I. Devetak, P. Hayden, and A. Winter, "The mother of all protocols: Restructuring quantum information's family tree," arXiv:quant-ph/0606225. 6. I. Devetak, A. W. Harrow, and A. J. Winter, "A resource framework for quantum Shannon theory," IEEE Transactions on Information Theory IT--54, 4587-4618 (2008).
	T, 5-5	Update on special topics
	Th, 5-7	No lecture