Quantum Introduction - Outlines

Currently it is a working draft.

Before applying consult with your teacher or professor, as every misused didactic material may result in misunderstanding and discouragement.

Any questions, comments, suggestions or remarks? moc.liamg|ladgimp#moc.liamg|ladgimp

Philosophy

(but with some experimental footing)

My general approach is to start with (classical) polarization of light, as it is a thing that:

  • is simple and can be visualized geometrically,
  • can be directly shown (e.g. with polarizations sheets, which I have).

And IMHO starting with classical mechanics (continuous variables) is the WORST approach, as it is:

  • difficult and
  • seeds some wrong intuitions.

Books

Valerio Scarani, Six Quantum Pieces: A First Course in Quantum Physics
http://www.amazon.com/Six-Quantum-Pieces-Course-Physics/dp/9814327549
In my opinion it looks great as an introduction to QM.
There is one in ICFO, I thinki in the hands of Alejandra Valencia or or Marta Garcia.

And just in case:

  • Simon Singh, The Code Book (a qeneral intro to cryptography; also at ICFO)
  • Carl D. Meyer, Matrix Analysis and Applied Linear Algebra (a general intro/reference to linear algebra; also here:http://www.matrixanalysis.com/DownloadChapters.html, very simply and didactically written)

Other materials

1-D Quantum Mechanics
http://www.falstad.com/qm1d/ (on http://www.falstad.com/mathphysics.html)
BTW: Play with it (it is nice also for older kids; at least I am in love with it); you can easily create coherent or squeezed states for the harmonic oscillator potential.

From the same site, also Ripple Tank is marvelous:
http://www.falstad.com/ripple/
You can see the interference, the total internal reflection, the lensing, the Fresnel zone plates, the Doppler effect, the scattering and many, many other phenomena.

My (humble) slides on the polarization of light:
http://dl.dropbox.com/u/17968211/polarization-of-light.zip
(they work well with actually showing phenomena, I always bring my polarization sheets).

Courses

7th Scientific Summer School, Olsztyn (Poland), 2011

"Quantum optics" on "7th Scientific Summer School" (I camp that I co-organized)
8-18 Aug 2011, Olsztyn, Poland
http://warsztatywww.wikidot.com/www7:optyka-kwantowa
(3h x 3 day workshop for talented high-schools students; there were difficult qualification tasks both as a strong filter and to teach preliminary materials (complex numbers (including radial representation), basics of linear algebra, quantum jargon (bras, kets and daggers))).

Outline:

1. Polarization of light
What is that, how can we act on it (wave plates, polarizers, rotation by a solution of sugar, …); also: the 3 polarizers "paradox".
2. Quants and measurement
Single photons behave in the same as a classical wave, just they can't be measured partially, only 0/1. And then the quantum measurement is the most intuitive interpolation of the classical measurement.
3. Superposition vs mixture
How to tell the difference using interference. Detection of the light-sensitive bomb.
4. Entanglement
What is that? Why it is the most intuitive approach to more particles? Relation between interference, entanglement and looking at objects.

Notes by one of the participants:
http://dl.dropbox.com/u/17968211/www7quantum_notes_by_lis.zip

There were ~6 participants. It went _really_ well (though I had a lot of luck to get so outstanding participants).
Also, it can be made a bit simpler, with less mathematics.

Programma Jonevs y Ciencia, ICFO, 2011

"Programma Jonevs y Ciencia"
15.06-15.07.2011, ICFO, Castelldefels (Barcelona)

6h twice a week
2 participants
with one it went great

General idea:

  • Rather involve and inspire than merely give lectures.
  • Use Python (or Mathematica) to actually test different cryptographic protocols (and sometimes - a coin), It's more convincing for high-school students to see things actually working than proving things.
  • "(*)" denotes that it's extra material that can be easily dropped without any harm to the rest.
  • Give simple homework exercises (given printed or in pdf, with lecture notes).
  • Don't use more formalism/mathematics than it's necessary.
  • Flexibly change the program according to their skills and interests.

Legend:

(*) - an additional material that I used
(**) - an additional material that I didn't use

Classical cryptography

1.1. Naive letter/word relabeling

  • give some interesting historical examples
  • as an example use rot13
  • (**) show that natural languages can be easily detected (with analysis of ngrams - i.e. frequencies of short strings of letters)

1.2. Perfect: XOR

  • show that is is perfect
  • no difference between the message and the key
  • practice on black&white images
  • and on words (character -> 8 bits -> encoding -> sending -> decoding -> 8 bits -> character)
  • but how to distribute the key?

1.3 (**) RSA

  • modulo, factorability
  • asymmetric codes, the actual RSA procedure
  • it's hard to break but not impossible (give time estimations with _current_ technology)

Quantum cryptography

2.1. Measurement of the (classical) polarization of light

  • (*) introduction to complex numbers
  • description of polarization with two numbers
  • polarizer, measurement of intensity, cos^2(alpha)
  • rotation of polarization (e.g. with half wave plates)
  • 2x2 matrices, how one can describe rotations and measurements with them
  • decomposition of a vector in different bases

2.2. Introduction to quantum mechanics (of two polarizations)

  • but what if there are no 'intensities' but only counts of single photons?
  • superposition vs mixture

2.3. BB84 protocol

  • 2 bases, the actual protocol
  • why Eve cannot simply eavesdrop without influencing noise
  • how to estimate number of bits which can be in hands of Eve
  • (*) 3 bases

2.4. (**) Quantum entanglement

  • Bell pairs, how to deal with them mathematically
  • classical correlations or more
  • Bell inequality (including futile trails to break it )
  • nonlocal boxes
  • quantum teleportation

2.5 (**) Information theory

  • Shannon entropy; when one can compress a file, how to play in "twenty questions" game
  • how to quantize the sent information (quantum or classical), when there is noise in the channel
  • how to check if information is altered and how to fix it (check sum, Hamming codes)
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