6.453 | Fall 2016 | Graduate
Quantum Optical Communication

Readings and Lecture Slides

Readings and Lecture Slides for each session of the course can be found below. Supplementary readings on probability (PDF) and random processes (PDF) are also available.

SES # TOPICS READINGS LECTURE SLIDES
1

Technical Overview

  • Optical eavesdropping tap - quadrature-noise squeezing
  • Action at a distance - polarization entanglement
  • Long-distance quantum state transmission - qubit teleportation

Session 1 Reading (PDF) Session 1 Lecture Slides (PDF)
2

Fundamentals of Dirac-Notation Quantum Mechanics

  • Quantum systems
  • States as ket vectors
  • State evolution via Schrödinger’s equation
  • Quantum measurements - observables

Session 2 Reading (PDF) Session 2 Lecture Slides (PDF)
3

Fundamentals of Dirac-Notation Quantum Mechanics

  • Definitions and axioms - reprise
  • Quantum measurements - statistics
  • Schrödinger picture versus Heisenberg picture
  • Heisenberg uncertainty principle

Session 3 Reading (PDF) Session 3 Lecture Slides (PDF)
4

Quantum Harmonic Oscillator

  • Quantization of a classical LC circuit
  • Annihilation and creation operators
  • Energy eigenstates - number-state kets

Session 4 Reading (PDF) Session 4 Lecture Slides (PDF)
5

Quantum Harmonic Oscillator

  • Number measurements versus quadrature measurements
  • Coherent states and their measurement statistics

Session 5 Reading (PDF) Session 5 Lecture Slides (PDF)
6

Quantum Harmonic Oscillator

  • Quadrature-representation wave functions
  • Minimum uncertainty-product (MUP) states
  • Squeezed states and their measurement statistics

Session 6 Reading (PDF) Session 6 Lecture Slides (PDF)
7

Quantum Harmonic Oscillator

  • Quadrature-measurement statistics and phase space
  • Characteristic functions and the Wigner distribution
  • Positive operator-valued measurement of â

Session 7 Reading (PDF) Session 7 Lecture Slides (PDF)
8

Quantum Harmonic Oscillator

  • Positive operator-valued measurement (POVM) of â
  • Reconciling POVMs and observables

Single-Mode Photodetection

  • Direct Detection - semiclassical versus quantum
  • Homodyne Detection - semiclassical versus quantum

Session 8 Reading (PDF) Session 8 Lecture Slides (PDF)
9

Single-Mode Photodetection

  • Direct Detection - reprise
  • Homodyne Detection - reprise
  • Heterodyne Detection - semiclassical versus quantum
  • Realizing the â measurement

Session 9 Reading (PDF) Session 9 Lecture Slides (PDF)
10

Single-Mode Photodetection

  • Signatures of non-classical light
  • Squeezed-state waveguide tap

Session 10 Reading (PDF) Session 10 Lecture Slides (PDF)
11

Single-Mode Photodetection

  • Squeezed-state waveguide tap - reprise

Single-Mode Linear Systems

  • Attenuators
  • Phase-Insensitive Amplifiers

Session 11 Reading (PDF) Session 11 Lecture Slides (PDF)
12

Single-Mode and Two-Mode Linear Systems

  • Attenuators
  • Phase-Insensitive Amplifiers
  • Phase-Sensitive Amplifiers
  • Entanglement

Session 12 Reading (PDF) Session 12 Lecture Slides (PDF)
13

Two-Mode Linear Systems

  • Parametric amplifier statistics
  • Entanglement

Four-Mode Quantum Systems

  • Polarization entanglement
  • Qubit teleportation

Session 13 Reading (PDF) Session 13 Lecture Slides (PDF)
14

Teleportation

  • Polarization entanglement and qubit teleportation
  • Quadrature entanglement and continuous-variable teleportation

Session 14 Reading (PDF) Session 14 Lecture Slides (PDF)
15

Teleportation

  • Fidelity analysis of continuous-variable teleportation

Session 15 Reading (PDF) Session 15 Lecture Slides (PDF)
16

Quantum Cryptography

  • One-time pad cryptography
  • Bennett-Brassard protocol quantum key distribution
  • Clauser-Horne-Shimony-Holt form of Bell’s inequality
  • Ekert protocol quantum key distribution

Session 16 Reading (PDF) Session 16 Lecture Slides (PDF)
17

Quantization of the Electromagnetic Field

  • Maxwell’s equations
  • Plane-wave mode expansions
  • Multi-mode number states and coherent states

Session 17 Reading (PDF) Session 17 Lecture Slides (PDF)
18

Continuous-Time Photodetection

  • Semiclassical theory - Poisson shot noise
  • Quantum theory - photon-flux operator measurement
  • Direct-detection signatures of non-classical light

Session 18 Reading (PDF) Session 18 Lecture Slides (PDF)
19

Continuous-Time Photodetection

  • Noise spectral densities in direct detection
  • Semiclassical theory of coherent detection
  • Quantum theory of coherent detection
  • Coherent-detection signatures of non-classical light

Session 19 Reading (PDF) Session 19 Lecture Slides (PDF)
20

Nonlinear Optics of X(2) Interactions

  • Maxwell’s equations with a nonlinear polarization
  • Coupled-mode equations for parametric downconversion
  • Phase-matching for efficient interactions
  • Classical solutions

Session 20 Reading (PDF) Session 20 Lecture Slides (PDF)
21

Nonlinear Optics of X(2) Interactions

  • Coupled-mode equations for parametric downconversion
  • Phase-matching for efficient interactions
  • Classical and quantum solutions
  • Gaussian-state characterization

Session 21 Reading (PDF) Session 21 Lecture Slides (PDF)
22

Quantum Signatures from Parametric Interactions

  • Hong-Ou-Mandel dip produced by parametric downconversion
  • Polarization entanglement produced by parametric downconversion
  • Photon twins from parametric amplifiers

Session 22 Reading (PDF) Session 22 Lecture Slides (PDF)
23

More Quantum Optical Applications

  • Binary optical communication with squeezed states
  • Phase-sensing interferometry with squeezed states
  • Super-dense coding with entangled states
  • Quantum lithography with “N00N” states

Session 23 Reading (PDF) Session 23 Lecture Slides (PDF)
Course Info
As Taught In
Fall 2016
Level
Learning Resource Types
assignment_turned_in Problem Sets with Solutions
notes Lecture Notes