Importance notice: undergrad students who want to get credits next semester at this course, please contact Sandra at cgif@if.usp.br.
This page contains all information about the 2018 graduate course in Quantum Information and Quantum noise.
Lectures will be on Mondays and Wednesdays, from 16:00 to 18:00, at Auditório Sul.
Lecture Notes: here are all notes in a single PDF.
Below they are divided into separate PDFs.
01 - Review of Quantum Mechanics.
Additional reading: chapter 2 of Nielsen and Chuang; chapter 2 of Preskill.
02 - Density Matrix theory.
Additional reading: Sec. 2.4 of Nielsen and Chuang and Sec. 2.3 of Preskill.
03 - Entanglement.
Additional reading: Secs. 2.4 and 2.5 of NC and Secs. 2.3 and 2.4 of Preskill.
04 - Reduced density matrices and Schmidt decomposition.
Additional reading: Secs. 2.4 and 2.5 of NC and Secs. 2.3 and 2.4 of Preskill.
05 - Entropies.
Additional reading: chapter 11 of NC and Secs. 5.1 and 5.2 of Preskill.
06 - POVMs and generalized measurements.
Additional readon: Secs. 2.2 and 2.4 of NC, Sec. 3.1 of Preskill and Sec. 2.2 of Gardiner and Zoller.
07 - Continuous variables.
arXiv 1401.4679.
08 - Quantum phase space.
Gardiner and Zoller, chapter 4.
09 - Lossy cavities.
10 - Quantum operations.
Nielsen and Chuang, chap. 8. Preskill Sec. 3.3.
11 - Lindblad master equations.
Preskill, Sec. 3.5. Breuer and Petruccione Sec. 3.1 and 3.2
For a nice (very) recent paper on divisibility (semigroup stuff), see arXiv 1805.00920
12 - Microscopic derivations.
I based these notes on chap. 5 of “Open Quantum Systems: an Introduction” of Rivas and Hulega.
See also Sec. 3.3 of Breuer and Petruccione.
Cool papers mentioned in class: arXiv 1711.01640 (optomechanics) and arXiv 1711.00582 (Rabi).
13 - Examples of microscopic derivations.
Chapter 3 of Breuer and Petruccione discuss several applications. The spin-boson model is discussed in chapter 4.
The discussion here is based on the original paper arXiv:quant-ph/9702001.
14 - Gaussian systems.
For all kinds of things related to Gaussian systems, have a look at the book “Quantum Continuous Variables” by
Alessio Serafini.
15 - Optomechanics.
A good book on optomechanics is that of Aspelmeyer, Kippenberg and Marquadt, entitled (not surprisingly)
“Cavity Optomechanics”
16 - Qubits in a common environment (Jader P. Santos).
For additional discussions on this type of model, see arXiv:quant-ph/0610140 and arXiv:1311.0018.
17 - Quantum Darwinism: sorry guys, I didn’t have time to write down the notes on this lecture.
The Zurek paper I mentioned in class is arXiv:0903.5082, from which you can find many other references. The
solution of the oscillator model we discussed is given in the Supplemental Material of arXiv:1804.02970.
18 - Bell and Leggett-Garg inequalities.
The paper about is in PRL 120 210402 (2018). The paper about Bell measurements in continuous variables, that
one of the students mentioned, is 1801.03194
19 - Quantum Estimation Theory (Jader P. Santos).
Problem sets:
- Problem set 3.
Notes on the Duan criteria.
Additional resources:
- Qulib library: This is a Mathematica Library with some useful functions for doing problems in Quantum Information and Open quantum systems.
To Install qulib, read these instructions.