COT6602 Quantum Information Theory

Term: Spring 2008
Time: Tues & Thurs 12:00pm - 1:15pm
Location: HEC302

Instructors: Anura Abeyesinghe and Pawel Wocjan
Office hours: Anura Abeyesinghe (Thurs 2:30pm - 3:45pm) and Pawel Wocjan (Tues & Thurs 2:30pm - 3:45pm)

Topics to be covered

Advanced Topics for Final Presentations


Book:
The required text book is M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge, 2000. This book covers all the topics in `Introduction and Tools' and few of the topics in `Noiseless Quantum Shannon Theory' and `Noisy Quantum Shannon Theory'. All other topics are covered in Unification of Quantum Information Theory (Ph.D. thesis by Anura Abeyesinghe) and references therein.

Grading Policy:
The final grade will be determined as follows: Homework Assignments 50%; Midterm Exam 25%; Final Presentation 25%

Grades A, B, C, D, and F are based on the straight-percentage scale (that is, 90% or above is A, 80% to 89.99% is B, etc.)

To enhance your learning experience and to help you solve the homework problems, you are encouraged to work in study groups of two to four people. However, you are required to turn in the solutions on your own, and you must never copy the solutions of other students.

No late homework and make-up tests will be accepted except for exceptional situations (handeled individually). The midterm exam is closed books, closed notes, and no calculators.

Please read and understand student rights and responsibilities including conduct rules clearly stated in UCF’s golden rules, at http://www.goldenrule.sdes.ucf.edu/2e_Rules.html


Announcements

Lectures

  Topic Readings Notes
Lecture #1 (01/08) Overview of Quantum Information Science
Review of Linear Algebra
NC pages 61 - 79
 
Lecture #2 (01/10) Review of Linear Algebra
Introduction to Quantum Mechanics
NC pages 80 - 96 and 98 - 111
 
Lecture #3 (01/15) Schmidt Decomposition
Density Operators
Reduced Density Operators
Purifications
NC pages 356 - 373 and 84 - 92
 
Lecture #4 (01/17) Quantum Operations
POVM Measurements
Generalized Measurements
Introduction to Shannon Entropy and von Neuman Entropy
Joint Entropy
Conditional Entropy
Relative Entropy
Mutual Information
NC Chapter 11
 
Lecture #5 (01/22) Klein's Inequality
Joint Entropy Theorem
Subadditivity
Triangle Inequality
Concativity
Strong Subadditivity and its consequences etc.
NC page 86 and pages 528 - 535
 
Lecture #6 (01/24) Classical and Quantum Data Processing Inequalities
Indistinguishability of Quantum States and the No-Cloning Theorem
Accessible Information and the Holevo Bound
NC Chapter 9  
Lecture #7 (01/29) Applications of the Holevo bound
Fano's inequality and the Quantum Fano inequality
The Trace Distance and it's properties
NC Chapter 9  
Lecture #8 (01/31) Fidelity and it's properties
Relationships between the trace distance and fidelity
Continuity of entropy(Fannes's inequality)
Ensemble average fidelity and the entanglement fidelity
NC pages 536-542  
Lecture #9 (02/05) Properties of the entanglement fidelity
Revisiting the quantum Fano inequality
Quantum teleportation and superdense coding
Entanglement distillation and dilution
Introduction to classical data compression
NC Pages 542-546 and the solutions to Problem Set #1  
Lecture #10 (02/07) The Chebyshev inequality
The law of large numbers
The theorem of typical sequences
Proof of the noisy channel coding theorem
NC Pages 542-546 and 578-580  
Lecture #11 (02/12) Quantum data compression NC Pages 578-580  
Lecture #12 (02/14) Revisiting entanglement distillation and dilution    
Lecture #13 (02/19) Overview of noiseless quantum Shannon theory
Trade-offs in blind data compression
Description of the mostgeneral problem in visible data compression (generalized remote state preparation)
Pages 1-7 of Anura's thesis  
Lecture #14 (02/26) Trade-off coding and the the Quantum-Classical trade-off Pages 1-7 and 23-31of Anura's thesis  
Lecture #15 (02/28) Conditionally typical projectors
Frequency typical sequences
Properties of frequency typical projectors
Coding theorems and strong converse for quantum channels-Andreas Winter IEEE Vol.45,No.7  
Lecture #16 (03/04) The Father Protocol of noiselss quantum Shannon theory (one shot eSDC)    
Lecture #17 (03/06) The Father Protocol continued    
Lecture #18 (03/18) Optimality of one-shot eSDC and eRSP
Ensemble version of eSDC
Pages 29-31 and 31-40 of Anura's thesis  
Lecture #19 (03/20) Generalized remote state preparation Pages 190-197 of Elements of Information Theory- Cover and Thomas  
Lecture #20 (03/25) Overview of classical noisy channel coding
The theorem of jointly typical sequences
Pages 198-203 of Elements of Information Theory- Cover and Thomas  
Lecture #21 (03/27) Noisy Channel Coding    
Lecture #22 (04/01) Noisy Channel Coding continued
Source Channel Coding
Overview of sending classical information over noisy quantum channels
NC pages 554-557  
Lecture #23 (04/03) Classical information over noisy quantum channels NC page 558  
Lecture #24 (04/08) The additivity questions in QIT
Optimality of the product state capacity
   
Lecture #25 (04/10) Optimality of the product state capacity continued
The fundamental tasks of QIT
   
Lecture #26 (04/15) The QIT family tree
The Fully Quantum Slepian Wolf protocol (FQSW)
   
Lecture #27 (04/17) Obtaining the other protocols from FQSW    

Final Presentations

Student Topic
Amy Thompson Quantum Cryptography
Diego Valente Coherent Classical Communication
Chen-Fu Chiang On quantum capacity of erasure channel assisted by back classical communication
Hamed Ahmadi Equivalence of additivity questions in quantum information theory

Homeworks