**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.