1. AvH
Senior
Research
Grant +
Feodor
Lynen
Chist-Era DIQIP
EU IP SIQS
Advanced ERC Grant:
QUAGATUA
Advanced ERC Grant:
OSYRIS
SGR 874
EU FET-Proactive
QUIC
Report from the Frontiers of Atomic, Molecular and Optical Physics and Quantum Information
FNP
Polish Science Foundation
NCN
Narodowe Centrum Nauki
EU STREP EQuaM
John Templeton Foundation
FOQUS

2. ICFO – Quantum Optics Theory
Postdocs ICFO:
Alessio Celi (LGT, Gen. Rel.)
Tobias Grass (FQHE, Exact Diag.)
Pietro Massignan (Fermions, Disorder)
Miguel Angel García March (Gauge Fields)
Michał Tomża (Quant-chemistry):
Christian Gogolin (QI, D-wave computers)
Shi-Ju Ran (TNS, many body)
Jordi Tura (QI, many body)
James Quach (many body)
Alexis Chacón (Atto)
Manab Bera (QI)
Swapan Rana (QI)
PhD ICFO:
Samuel Mugel (QRandom Walks)
Aniello Lampo (Open Systems)
David Raventos (Gauge Fields)
Emanuelle Tirito (TNS)
Angelo Piga (TNS)
Nils-Eric Gűnther
Christos Charampoulos (Open Sys)
Noslen Suárez (Atto)
MPI Garching postdoc:
Arnau Riera (Qthermo, Qdyn)
Ex-members and collaborators:
François Dubin (CNRS), G. John Lapeyre (CSIC), Luca Tagliacozzo (Stathclyde), Matthieu Alloing (Paris), Tomek Sowiński (IFPAN), Phillip Hauke (IQOQI), Omjyoti Dutta (UJ, Cracow), Christian Trefzger (Paris); Kuba Zakrzewski (UJ, Cracow), Mariusz Gajda (IF PAN), Boris Malomed (Haifa), Ulrich Ebling (Kyoto), Bruno Julia Díaz (UB), Christine Muschik (IQOQI), Marek Kuś, Remigiusz Augusiak (CFT), Julia Stasińska (IFPAN), Alexander Streltsov (FUB), Ravindra Chhajlany (UAM), Fernando Cucchietti (MareNostrum), Anna Sanpera (UAB), Veronica Ahufinger (UAB)

3. ICFO (www.icfo.eu) Created on paper 2002, first employees 2004
ICFO (
Created on paper 2002, first employees 2004
14000 m2 labs space
23 groups (19 experimental, 4 theory)
Light for health, light for energy, light for information
Biophotonics, Nanophotonics, Quantum Optics, Nonblinear Optics
11 ERC Grants (9 Grantees)
1565 papers, cits., H-index 73
6 Nature, 5 Science, 4 PNAS, 57 Nature Group, 172 PRL
Our Director, Lluis Torner in his standard outfit

4. Quantum simulators
Ultracold atoms in optical lattices: Simulating quantum many-body physics
M. Lewenstein, A. Sanpera, V. Ahufinger, Oxford University Press (2012)

5. Lecture 1: Introduction to Quantum Information
AvH
Senior
Research
Grant +
Feodor
Lynen
Advanced ERC Grant:
QUAGATUA
Chist-Era DIQIP
EU IP SIQS
Lecture 1: Introduction to Quantum Information
Polish Science Foundation
EU STREP EQuaM
Hamburg
Theory
Prize
John Templeton Foundation
Advanced ERC Grant:
OSYRIS
ICFO-Cellex-Severo Ochoa

6. 1.1 Report from the Frontiers of QI - Outline
1.2 Entanglement theory:
Bipartite states
Entanglement criteria
Positive maps
Entanglement witnesses
Entanglement measures
1.3. Entanglement in many body systems
Computational complexity
Entanglement of a generic state
Area laws
Tensor network states
1.4. Non-locality in many body systems
Correlations – DIQIP approach
CHSH Inequality and its violations
Non-locality in many body systems
Many body physics from a quantum information perspective R. Augusiak, F. M. Cucchietti, M. Lewenstein Lect. Notes Phys. 843, (2010).
Ultracold atoms in optical lattices:
Simulating quantum many-body systems M. Lewenstein, A. Sanpera, V. Ahufinger Oxford University Press (2012)

7. 1.2.1 Entanglement Theory – Bipartite Pure States
Proof?

8. 1.2.2 Entanglement Theory – Bipartite Mixed States

9. 1.2.3 Entanglement Criteria

10. 1.2.4 Entanglement Criteria – Partial Transposition

11. 1.2.5 Entanglement Witnesses and Hahn-Banach Theorem

12. 1.2.5 Entanglement Witnesses and Hahn-Banach Theorem

13. 1.2.6 Positive Maps and the Entanglement Problem

14. 1.2.6 Positive Maps and the Entanglement Problem
Proof?

15. 1.2.7 Positive Maps and Entanglement Witnesses

16. 1.2.7 Positive Maps and Entanglement Witnesses
Proof?

17. 1.2.7 Entanglement Measures – Pure States

18. 1.2.7 Entanglement Measures – Entanglement of Formation

19. 1.2.7 Entanglement Measures – Concurrence

20. 1.2.7 Entanglement Measures – Negativity/Logarithmic Negativity

21. 1.3 Entanglement in Many Body Systems

22. 1.3.1 Computational complexity
Classical simulators:
What can be simulated classically?
What is computationally hard (examples)?
Ultracold atoms in optical lattices: Simulating quantum many-body physics,
M. Lewenstein, A. Sanpera, V. Ahufinger, in print Oxford University Press (2012)

23. 1.3.1 What can be simulated classically?
Quantum Monte Carlo
Systematic perturbation theory
Exact diagonalization
Variational methods (mean field, MPS, PEPS
MERA, TNS…)

24. 1.3.1 What is computationally hard?
Fermionic models
Frustrated systems
Disordered systems
Quantum dynamics

25. 1.3.2 Why computations are hard? Entanglement of a generic state
Proof?

26. 1.1.3 Why there are some hopes? - Area laws
Classical area laws
Thermal area laws
Quantum area laws in 1D
Quantum area laws in 2D?

27. 1.1.3 Area laws Area law: Reduced density matrix of a region R
scales as the size of the boundary of R.

28. 1.1.3 Area laws for thermal states

29. 1.1.3 Quantum area laws in 1D

30. 1.3 Quantum area laws in 1D

31. ? One can prove generally S(ρA) ≤ |∂A| log(|∂A|)
1.3 Quantum area laws in 2D, 3D …
One can prove generally
S(ρA) ≤ |∂A| log(|∂A|) ?

32. 1.3.4 TNS and quantum many-body systems
Many-body quantum systems are difficult to describe.
We need coefficients to represent a state.
To determine physical quantitites (expectation values) an exponential
number of computations is required.

33. 1.3.4 Definition of TNS (MPS in 1D)
GHZ states:
where
maps
1D states:
as:
where
D-dimensional
are maximally entangled states
maps

34. Definition of TNS (MPS in 1D)
2D states:
maps
General:

35. Lecture 2: Introduction to Quantum Infomation Theory
AvH
Senior
Research
Grant +
Feodor
Lynen
Advanced ERC Grant:
QUAGATUA
Chist-Era DIQIP
EU IP SIQS
Lecture 2: Introduction to Quantum Infomation Theory
Polish Science Foundation
EU STREP EQuaM
Hamburg
Theory
Prize
John Templeton Foundation
Advanced ERC Grant:
OSYRIS
ICFO-Cellex-Severo Ochoa

36. Detecting Non-Locality in Many Body Systems
AvH
Senior
Research
Grant +
Feodor
Lynen
Chist-Era DIQIP
EU IP SIQS
Advanced ERC Grant:
QUAGATUA
Advanced ERC Grant:
OSYRIS
SGR 874
EU FET-Proactive
QUIC
Detecting Non-Locality in Many Body Systems
Solid State IFPAN
FNP
Polish Science Foundation
NCN
Narodowe Centrum Nauki
EU STREP EQuaM
John Templeton Foundation
FOQUS

37. ICFO – Quantum Optics Theory
Postdocs ICFO:
Alessio Celi (LGT, Gen. Rel.)
Tobias Grass (FQHE, Exact Diag.)
Pietro Massignan (Fermions, Disorder)
Miguel Angel García March (Gauge Fields)
Michał Tomża (Quant-chemistry):
Christian Gogolin (QI, D-wave computers)
Shi-Ju Ran (TNS, many body)
Jordi Tura (QI, many body)
James Quach (many body)
Alexis Chacón (Atto)
Manab Bera (QI)
Swapan Rana (QI)
PhD ICFO:
Samuel Mugel (QRandom Walks)
Aniello Lampo (Open Systems)
David Raventos (Gauge Fields)
Emanuelle Tirito (TNS)
Angelo Piga (TNS)
Nils-Eric Gűnther
Christos Charampoulos (Open Sys)
Noslen Suárez (Atto)
MPI Garching postdoc:
Arnau Riera (Qthermo, Qdyn)
Ex-members and collaborators:
François Dubin (CNRS), G. John Lapeyre (CSIC), Luca Tagliacozzo (Stathclyde), Matthieu Alloing (Paris), Tomek Sowiński (IFPAN), Phillip Hauke (IQOQI), Omjyoti Dutta (UJ, Cracow), Christian Trefzger (Paris); Kuba Zakrzewski (UJ, Cracow), Mariusz Gajda (IF PAN), Boris Malomed (Haifa), Ulrich Ebling (Kyoto), Bruno Julia Díaz (UB), Christine Muschik (IQOQI), Marek Kuś, Remigiusz Augusiak (CFT), Julia Stasińska (IFPAN), Alexander Streltsov (FUB), Ravindra Chhajlany (UAM), Fernando Cucchietti (MareNostrum), Anna Sanpera (UAB), Veronica Ahufinger (UAB)

38. Detecting non-locality in many body systems - Outline
0. Entanglement theory:
0.1 Bipartite pure states (Schmidt decomposition)
0.2 Bipartite mixed states
0.3 Entanglement criteria
0.4 Entanglement measures (entanglement entropy)
1. Entanglement in many body systems
1.1 Computational complexity
1.2 Entanglement of pure states (generic, and not…)
1.3 Area laws
1.4 Tensor network states
2. Non-locality in many body systems
2.1 Correlations – DIQIP approach
2.2 Non-locality in many body systems
2.3 Physical realizations with ultracold ions
2.4.Physical realizations with spin chains
Many body physics from a quantum information perspective R. Augusiak, F. M. Cucchietti, M. Lewenstein Lect. Notes Phys. 843, (2010).
Ultracold atoms in optical lattices:
Simulating quantum many-body systems M. Lewenstein, A. Sanpera, V. Ahufinger Oxford University Press (2012)

39. Quantum simulators, precise measurements and ultracold matter
Ultracold atoms in optical lattices: Simulating quantum many-body physics
M. Lewenstein, A. Sanpera, and V. Ahufinger, Oxford University Press (2012)

40. 2. Non-locality in Many Body Systems

41. 2. Non-locality in Many Body Systems
Courtesy of Ana Belén Sainz
paris.pdf
2. Non-locality in Many Body Systems
2.1 Correlations – DIQIP approach
2.2 Non-locality in many body systems
J. Tura, R. Augusiak, A.B. Sainz, T. Vértesi, M. Lewenstein, and A. Acín,
Detecting the non-locality of quantum many body states, arXiv: , Science 344, 1256 (2014).
J. Tura, A.B. Sainz, T. Vértesi, A. Acín, M. Lewenstein, R. Augusiak,
Translationally invariant Bell inequalities with two-body correlators, arXiv: ,
J. Phys. A: Math. Theor (2014), special issue of J. Phys. A on “50 years of Bell’s Theorem”.

49. nm + n(n-1)m2/2

54. R. Schmied, J. -D. Bancal, B. Allard, M. Faddel, V. Scarani, P
R. Schmied, J.-D. Bancal, B. Allard, M. Faddel, V. Scarani, P. Treutlein, and N. Sangouard, Science 352, 6284, 441 (2016).

58. Ana Belén Sainz

59. 2.3 Physical realizations with ultracold ions

60. 2.3 Realizations with ultracold ions/atoms

61. 2.3 Realizations with ultracold ions

62. 2.3 Realizations with ultracold ions

63. 2.3 Realizations with ultracold ions

64. Nonlocality in 1-D many-body Systems (spin chains)
J. Tura, G. de las Cuevas, R. Augusiak,
M. Lewenstein, A. Acín, J. I. Cirac
Nonlocality in 1-D many-body systems

65. Idea Start with a fermionic Hamiltonian
Exact diagonalization
Transformation to a spin Hamiltonian
Jordan-Wigner Transformation
Assign a Bell inequality in a natural way - Quantum bound ↔ Ground state energy
Translationally invariant. → Closed formulas.
Nonlocality in 1-D many-body systems

66. Classical bound? Dynamic programming
Very versatile optimization technique
Finding the optimal deterministic local strategy
Already optimized
Current step
Possible influence
to current step
Still irrelevant
measurements. Optimization at step .
Translationally invariant → Exponentially faster
Nonlocality in 1-D many-body systems

67. 1.3 Non-locality in Many Body Systems
J. Tura, R. Augusiak, A.B. Sainz, T. Vértesi, M. Lewenstein, and A. Acín,
Detecting the non-locality of quantum many body states, arXiv:  
J. Tura, A.B. Sainz, T. Vértesi, A. Acín, M. Lewenstein, R. Augusiak,
Translationally invariant Bell inequalities with two-body correlators, arXiv: ,
submitted to special issue of J. Phys. A on “50 years of Bell’s Theorem”.
Courtesy of Ana Belén Sainz
paris.pdf

68. Quantum simulators
Ultracold atoms in optical lattices: Simulating quantum many-body physics
M. Lewenstein, A. Sanpera, V. Ahufinger, Oxford University Press (2012)