New Course Offering - Information in a Photon

Professor Saikat Guha will be teaching a new course at UMD for the Spring 2025 semester. This course will be open to both graduate and undergraduate students, and will be ideal for ECE students who would like to get a feel for why quantum treatment of light in the contexts of information processing (digital communications, sensing, imaging, etc.) offers fundamentally more powerful insights, and the design of systems with better performance than what is possible otherwise. No prior background in quantum mechanics, optics or information theory is necessary, but students who have a strong background in probability and linear algebra will find it the easiest to navigate the material.

ENEE 439G/739G: Information in a Photon

ECE Special Topics Course

Syllabus, Pre-requisites, and Course Objectives

Overview

The goal of this course is to develop a rigorous understanding of the fundamental limits of the efficiency with which one can encode information in, and extract information from light, broadly in the contexts of communications and sensing.

To develop this understanding, the course covers:

• Information Theory: Basics of the concept of information theory.
• Estimation and Detection Theory: Essential aspects of these theories.
• Optical Modes and Interference: Mathematical descriptions of orthogonal optical modes and interference.
• Noise in Photodetection: Analysis as per the semiclassical theory of photodetection.

The course explores examples from communications and sensing, demonstrating how:

1. Optical domain pre-processing of information-bearing light, and
2. Novel receiver designs
   …can enhance information encoding and extraction compared to conventional means.

It introduces the concept of “quantum limits” of information processing, exploring the best possible efficiency for encoding information in light as permitted by physical laws.

Course Objectives

Students will develop an appreciation for the advantages of treating light as a quantum mechanical object to glean richer information compared to classical electromagnetic wave treatments.

Primary Goals:

• Equip students with deep intuitions on optical detection, laying the groundwork for research in quantum-enhanced photonic information processing.
• Develop an understanding of:
  1. The value of quantum treatments of light to find the fundamental limits of encoding information.
  2. How pre-detection manipulation of light can optimize information extraction.

This course assumes no background in optics, stochastic processes, quantum mechanics, information theory, or estimation theory. However, students should have proficiency in:

• Complex numbers
• Probability theory
• Linear algebra (vectors and matrices)

Pre-requisites

• Basic Fundamentals: ENEE101
• Probability Theory: ENEE324 (or equivalent)
• Linear Algebra: ENEE290 or MATH461 (advanced option)

A background in quantum mechanics is not required but can be helpful.

Assignments

Homeworks

• Weekly problem sets, due the following week in class.

Advanced Problems

• Graduate Students:
  • Solve one of ~20 Advanced Problems during the semester.
  • Present the solution at an end-of-semester workshop.
  • Advanced Problems include open-ended components that may lead to publishable research.
• Undergraduate Students:
  • Advanced Problems are fully optional.

Grades

• Undergraduate Students:
  • Midterm Exams: 50%
  • Homework: 50%
• Graduate Students:
  • Midterm Exams: 40%
  • Homework: 30%
  • Advanced Problem: 30%

Grades will be assigned on separate curves for undergraduate and graduate students.

Detailed Course Description

Modules Overview

The course is divided into three modules, each approximately 10 lectures.

Module 1: Pre-Detection Transformations of Information-Bearing Light

• Quasimonochromatic laser light pulse and photon detection statistics.
• Linear interferometric transformations and optical-domain manipulations.
• Use of electro-optic feedback during detection.
• Binary state discrimination and quantum-optimal receiver designs.
• Introduction to quantum states of an optical mode (coherent states and number states).
• Open problems in quantum state discrimination.

Module 2: Joint Detection Receiver for Optical Communications

• Brief introduction to classical information theory and Shannon capacity.
• Novel optical detection methods for laser-light modulated communications.
• Joint detection receivers and superadditivity in communications capacity.
• Modulation formats, error correction codes, and decoding algorithms.
• Derivation of the “quantum limit” of communications capacity.
• Open problems in error correction codes and receiver designs.

Module 3: Novel Receivers for Optical Sensing and Imaging

• Introduction to detection theory, Fisherian, and Bayesian estimation theories.
• Applications to optical phase estimation and quantum-enhanced sensing.
• Standard quantum limit vs. Heisenberg limit for phase estimation.
• Applications in photonic sensors (gyroscopes, RF sensors, beam deflection).
• Fundamental “quantum limits” of sensing.
• Passive imaging and novel telescope receiver designs for higher resolution.

Conclusion

The course concludes with a discussion of research avenues in:

• Quantum optics
• Quantum information theory
• Photonic quantum information processing

Advanced mathematical principles needed for future graduate-level courses will also be outlined.