## Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

## About This Course

Welcome to *6.453 Quantum Optical Communication*. It is one of a collection of MIT classes that deals with aspects of an emerging field known as quantum information science. As you can divine from its title, this course is about quantum communication, rather than quantum computation, although both of these topics fall under the general rubric of quantum information science. Moreover, this course is far from being an entirely abstract presentation of quantum communication (although such a development is indeed possible) but is instead intimately tied to quantum optics. Finally, this course does not presume a deep background in quantum mechanics or optics, such as would be obtained from one or more semesters of study in the Physics Department, but instead teaches all the basic quantum mechanics that is needed and does not require any electromagnetics knowledge beyond the plane-wave solutions to Maxwell's equations in a source-free region of empty space.

## Prerequisites

The preceding paragraph characterizes the course as an outgrowth of quantum optics, i.e., the marriage of quantum mechanics and optics. An alternative, and more informative, way to look at the course is as an outgrowth of communications and especially communication theory. This should be clear from its prerequisites being *6.011 Introduction to Communication, Control, and Signal Processing* and *18.06 Linear Algebra*, which indicate that this course will build on knowledge of signals and systems, probability, and linear algebra. In particular, we will rely on Fourier transforms, convolutions, probability mass functions, probability density functions, mean values, variances, vectors, matrices, eigenvalues, and eigenvectors. These topics will not be reviewed in the lectures. Instead, they will be probed on Problem Set 1. The supplementary reading for this problem set may help you review, but it is probably better (and easier) if you refer to the course materials you have from wherever and whenever you learned basic signals and systems, probability, and linear algebra.

## Textbook

There is no required text. Readings will be provided, along with suggestions for supplementary reading.

## Assignments and Grading

There will be eight problem sets and an in-class mid-term quiz but there will not be a final examination. A term paper will be required.

ASSIGNMENTS | PERCENTAGES OF GRADES |
---|---|

Problem Sets | 20% |

Mid-Term Quiz | 40% |

Term Paper | 40% |

*Note: The term paper is not avalibable to OCW users.*

## Course Outline

SUBJECTS | TOPICS |
---|---|

Quantum Optics | Dirac notation quantum mechanics; harmonic oscillator quantization; number states, coherent states, and squeezed states; representation and classical fields |

Single-Mode and Two-Mode Quantum Systems | Direct, homodyne, and heterodyne detection; linear propagation loss; phase insensitive and phase sensitive amplifiers; entanglement and teleportation |

Multi-Mode Quantum Systems | Field quantization; quantum photodetection |

Nonlinear Optics | Phase-matched interactions; optical parametric amplifiers; generation of squeezed states, photon-twin beams, non-classical fourth-order interference, and polarization entanglement |

Quantum System Theory | Optimum binary detection; quantum precision measurements; and quantum cryptography |

## Calendar

SES # | TOPICS | ASSIGNMENTS |
---|---|---|

1 | Technical Overview | |

2 | Fundamentals of Dirac-Notation Quantum Mechanics I | |

3 | Fundamentals of Dirac-Notation Quantum Mechanics II | Problem Set 1 Due |

4 | Quantum Harmonic Oscillator I | |

5 | Quantum Harmonic Oscillator II | Problem Set 2 Due |

6 | Quantum Harmonic Oscillator III | |

7 | Quantum Harmonic Oscillator IV | Problem Set 3 Due |

8 | Quantum Harmonic Oscillator V | |

9 | Single-Mode Photodetection I | Problem Set 4 Due |

10 | Single-Mode Photodetection II | Problem Set 5 Due |

11 | Single-Mode Photodetection III | |

12 | Single-Mode and Two-Mode Linear Systems | Problem Set 6 Due |

13 | Two-Mode Linear Systems | |

14 | Teleportation I | Problem Set 7 Due |

15 | Teleportation II | |

16 | Quantum Cryptography | Problem Set 8 Due; Midterm Exam |

17 | Quantization of the Electromagnetic Field | |

18 | Continuous-Time Photodetection I | |

19 | Continuous-Time Photodetection II | |

20 | Nonlinear Optics of X^{(2)} Interactions I | |

21 | Nonlinear Optics of X^{(2)} Interactions II | |

22 | Quantum Signatures from Parametric Interactions | |

23 | More Quantum Optical Applications | Term paper Due |