Advanced ERC Grant: QUAGATUA

1. AvH Senior Research Grant + Feodor Lynen Advanced ERC Grant: QUAGATUA EU IP SIQS Chist-Era DIQIP Maciej Lewenstein Detecting Non-Locality in Many Body Systems Enrico Fermi School Course 191 Polish Science Foundation EU STREP EQuaM Hamburg Theory Prize John Templeton Foundation Advanced ERC Grant: OSYRIS ICFO-Cellex-Severo Ochoa

2. ICFO – Quantum Optics Theory Postdocs ICFO: AlessioCeli (LGT, Gen. Rel.) Tobias Grass (FQHE, Exact Diag.) RemigiuszAugusiak (QI, ManyBody) Pietro Massignan (Fermions, Disorder) G. John Lapeyre (QI, Statphys) Luca Tagliacozzo (LGT, TNS, QDyn) Christine Muschik (TQNP) Alex Streltsov (QI) ArnauRiera (QThermo, QDyn) PierrickCheiney (Art. Graphene, exp) PhD ICFO: Ulrich Ebling (Fermions) Alejandro Zamora (MPS,LGT) Piotr Migdał (QI, QNetworks) Jordi Tura (QI, many body) Mussie Beian (Excitons, exp) Samuel Mugel (Art. Graphene) Aniello Lampo (Open Systems) David Raventos (Gauge Fields) Caixa-Manresa-Fellows: Julia Stasińska (QI, Disorder) Polish postoc grants Ravindra Chhajlany (Hubbard Models) MPI Garching postdoc: Andy Ferris (TNS, Frustrated AFM) Stagiers (en français) Michał Maik (Dipolar gases) Anna Przysiężna (Dipolar gases)

3. Detecting non-locality in many body systems - Outline 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 Ultracold atoms in optical lattices: Simulating quantum many-body systems M. Lewenstein, A. Sanpera, V. Ahufinger Oxford University Press (2012) Many body physics from a quantum information perspective R. Augusiak, F. M. Cucchietti, M. Lewenstein Lect. Notes Phys. 843, 245-294 (2010).

4. 1. Entanglement in Many Body Systems

5. 1.1 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)

6. 1.1 What can be simulated classically? • Quantum Monte Carlo • Systematic perturbation theory • Exact diagonalization • Variational methods (mean field, MPS, PEPS MERA, TNS…)

7. 1.1 What is computationally hard? • Fermionic models • Frustrated systems • Disordered systems • Quantum dynamics

8. 1.2 Entanglement of pure states “Good” entanglement measure for pure states Take reduced density matrix: ρA = TrB(ρAB) = TrB(|ΨAB›‹ΨAB|), and then take von Neumann entropy E(|ΨAB›‹ΨAB|) = S(ρA) = S(ρB), where S(ρ) = -Tr(ρ log ρ). Note that maximally entangled states have E(|ΨAB›‹ΨAB|) = log dA Note: For mixed states a super hard problem…

9. 1.2 Why computations may be hard? Entanglement of a generic state

10. 1.2 Why computations may be hard? Entanglement of a generic state

11. 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?

12. 1.3 Area laws A B • Area law: Averaged values of correlations, between the regions A and B, scale as the size of the boundary of A. For instance for quantum pure (ground states): S(ρA) ~ ∂A (Jacob Beckenstein, Mark Srednicki…)

13. 1.3 Area laws for thermal states A B

14. 1.3 Quantum area laws in 1D

15. 1.3 Quantum area laws in 1D

16. 1.3 Quantum area laws in 2D, 3D … One can prove generally S(ρA) ≤ |∂A| log(|∂A|) ?

17. Many-body quantum systems are difficult to describe. 1.4 TNS and quantum many-body systems We need coefficients to represent a state. • To determine physical quantitites (expectation values) an exponential number of computations is required.

18. 1.4 Definition of TNS (MPS in 1D) GHZ states: where maps 1D states: as: where D-dimensional are maximally entangled states maps

19. 1) Open boundary conditions: It coincides with DMRG 2) Periodic boundary conditions: (Verstraete, Porras, Cirac, PRL 2004) It outperforms DMRG

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

21. 2. Non-locality in Many Body Systems

22. 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:1306.6860, 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:1312.0265, in print to special issue of J. Phys. A on “50 years of Bell’s Theorem”. Courtesy of Ana Belén Sainz paris.pdf • 2.1 Correlations – DIQIP approach • 2.2 Non-locality in many body systems

32. Analytic example: Family of many body Bell inequalities

41. 2.3 Physical realizations with ultracold ions

42. 2.3 Realizations with ultracold ions/atoms

43. 2.3 Realizations with ultracold ions

44. 2.3 Realizations with ultracold ions

45. 2.3 Realizations with ultracold ions

46. 2.3 Realizations with ultracold ions

47. Detecting non-locality in many body systems - Conclusions • Entanglement in many body systems • “Weak” entanglement ≈ Area laws ≈ Classical computability! 2. Non-locality in many body systems • “Weak” entanglement ≈ Locality with respect to “simple” Bell inequalities. • “Strong” non-locality and symmetry ≈ Classical computability? Ultracold atoms in optical lattices: Simulating quantum many-body systems M. Lewenstein, A. Sanpera, V. Ahufinger Oxford University Press (2012) Many body physics from a quantum information perspective R. Augusiak, F. M. Cucchietti, M. Lewenstein Lect. Notes Phys. 843, 245-294 (2010).

48. Quantum Optics Theory ICFO Hits 2013-2014

49. Shakin‘ and artificial gauge fields

50. Shakin‘ and artificial gauge fields