**MACIEJ LEWENSTEIN**

**Quantum Optics Theory group**

ICFO-The Institute of Photonic Sciences

ICFO-The Institute of Photonic Sciences

Basics of quantum information: entanglement in bipartite systems, entanglement criteria; entanglement witnesses; linear maps and Jamiołkowski-Choi-Sudarshan isomorphism; sufficient entanglement criteria. **
Theory Lecture, September 29, 2015, 10:15. Blue Lecture Room**

Basics of quantum information: measurements: von Neumann, POVMs, channels; operations: LOCC, separable, stochastic separable, SLOCC; J-C-S isomorphism for operations; entanglement measures: pure states, operational entanglement measures; convex roof entanglement measures; entanglement in many body systems: entanglement in two body reduced density matrix, localizable entanglement; entanglement entropy. **
Theory Lecture, October 6, 2015, 10:15. Blue Lecture Room**

Basics of quantum information: entanglement in many body systems: entanglement in two body reduced density matrix, localizable entanglement; entanglement entropy and entanglement spectrum; entanglement in multipartite systems; three parties; genuine multipartite entanglement witnesses and checks; Fisher information and its role in metrology; quantum Fisher information and entanglement. Open problems. **
Theory Lecture, October 13, 2015, 10:15. Blue Lecture Room**

Basics of quantum information: non-locality; device independent characterization of correlations: Non-signaling correlations, quantum correlations and local correlations; Bell’s theorem, Bell and Clauser-Horne- Shimony-Holt (CHSH) inequality; current status of knowledge: which states are non-local? Non-locality in quantum many body systems; derivation of permutation symmetric and translationally invariant Bell inequalities; open problems. **
Theory Lecture, October 20, 2015, 10:15. Blue Lecture Room (Lecturer: M. Lewenstein/Jordi Tura) **

Strongly-interacting quantum gases: BEC-BCS crossover**
Theory Lecture, October 27, 2015, 10:15. Blue Lecture Room (Lecturer: Pietro Massignan) **

Strongly-interacting quantum gases: variational Ansaetze**
Theory Lecture, November 3, 2015, 10:15. Blue Lecture Room (Lecturer: Pietro Massignan) **

Strongly-interacting quantum gases: derivation and properties of the universal (Tan\'s) relations**
Theory Lecture, November 10, 2015, 10:15. Blue Lecture Room (Lecturer: Pietro Massignan) **

Strongly-interacting quantum gases: universal thermodynamics**
Theory Lecture, November 17, 2015, 10:15. Blue Lecture Room (Lecturer: Pietro Massignan) **

Lieb-Robinson bounds - propagation of correlations in lattice systems**
Theory Lecture, November 24, 2015, 10:15. Blue Lecture Room (Lecturer: Christian Gogolin) **

Equilibration and thermalization - how to define them in closed quantum systems and what we know about them**
Theory Lecture, December 1, 2015, 10:15. Blue Lecture Room (Lecturer: Christian Gogolin) **

Structural properties of thermal states of spin and fermionic systems - when they can undergo phase transitions and how stable they are against local perturbations**
Theory Lecture, December 15, 2015, 10:15. Blue Lecture Room (Lecturer: Christian Gogolin) **

Bogoliubov\'s Inequality and beyond - proofs of the absence of phase transitions in 1D systems**
Theory Lecture, January 12, 2016, 10:15. Blue Lecture Room (Lecturer: Christian Gogolin) **