Information in a Photon

  • Course Type: Graduate Course, Undergraduate Course
  • Semester Offered: Spring
Course Number: 
OPTI 495B/595B
Course Number: 
OPTI 595B/495B
Units: 
3
Distance Course: 
Yes
Course Description: 
This course will develop the mathematical theory of noise in optical detection from first principles, with the goal of understanding the fundamental limits of efficiency with which one can extract information encoded in light. We will explore how optical-domain interferometric manipulations of the information bearing light, i.e., prior to the actual detection, and the use of detection-induced electro-optic feedback during the detection process can alter the post-detection noise statistics in a favorable manner, thereby facilitating improved efficiency in information extraction. Throughout the course, we will evaluate applications of such novel optical detection methods in optical communications and sensing, and compare their performance with those with conventional ways of detecting light. We will also compare the performance of these novel detection methods to the best performance achievable---in the given problem context---as governed by the laws of (quantum) physics, without showing explicit derivations of those fundamental quantum limits. The primary goal behind this course is to equip students (as well as interested postdocs and faculty) coming from a broad background who are considering taking on theoretical or experimental research in quantum enhanced photonic information processing, with intuitions on a deeper way to think of optical detection, and to develop an appreciation of: (1) the value of a full quantum treatment of light to find fundamental limits of encoding information in the photon, and (2) how pre-detection manipulation of the information-bearing light can help dispose it information favorably with respect to the inevitable detection noise. This course will not assume any background in optics, stochastic processes, quantum mechanics, information theory or estimation theory. However, an undergraduate mathematical background and proficiency in complex numbers, probability theory, and linear algebra (vectors and matrices) will be assumed.
Prerequisite(s): 
1. Complex numbers; 2. Basic probability theory; 3. Elementary linear algebra. [This course should be accessible to most senior undergraduate and graduate students. Basic exposure to and proficiency in undergraduate mathematics will be assumed. If unsure, please contact instructor prior to registering.]
Instructor(s): 
Saikat Guha
Contact: 
 
Office Hours: 
1 hour every week and by appointment
Textbooks: 

No text book required. Printed handouts, and recommended reading will be distributed and will also be posted on the course website/D2L.

Attendance Policy: 
The UA’s policy concerning Class Attendance, Participation, and Administrative Drops is available at: http://catalog.arizona.edu/policy/class-attendance-participation-and-administrative-drop
 
The UA policy regarding absences for any sincerely held religious belief, observance or practice will be accommodated where reasonable, http://policy.arizona.edu/human-resources/religious-accommodation-policy.
 
Absences pre-approved by the UA Dean of Students (or Dean Designee) will be honored. See: https://deanofstudents.arizona.edu/absences
 
Participating in the course and attending lectures and other course events are vital to the learning process. As such, attendance is required at all lectures and discussion section meetings. Students who miss class due to illness or emergency are required to bring documentation from their health-care provider or other relevant, professional third parties. Failure to submit third-party documentation will result in unexcused absences.
Course Syllabus: 
Academic Integrity

According to the Arizona Code of Academic Integrity, “Integrity is expected of every student in all academic work. The guiding principle of academic integrity is that a student’s submitted work must be the student’s own.” Unless otherwise noted by the instructor, work for all assignments in this course must be conducted independently by each student. Co-authored work of any kind is unacceptable. Misappropriation of exams before or after they are given will be considered academics misconduct.

Misconduct of any kind will be prosecuted and may result in any or all of the following:

  • Reduction of grade
  • Failing grade
  • Referral to the Dean of Students for consideration of additional penalty, i.e., notation on a student’s transcript re: academic integrity violation, etc.
Students with Learning Disabilities

If a student is registered with the Disability Resource Center, he/she must submit appropriate documentation to the instructor if he/she is requesting reasonable accommodations.

The information contained in this syllabus may be subject to change with reasonable advance notice, as deemed appropriate by the instructor.