Quantum Information and Quantum Noise

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.  

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 

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 1.

- Problem set 2.

- 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

 © Gabriel Teixeira Landi 2018