1. ISTITUTO NAZIONALE DI RICERCA METROLOGICA Exploiting hidden correlations: the illusionist game Alice Meda Marco Genovese

2. ISTITUTO NAZIONALE DI RICERCA METROLOGICA 8 labs on quantum optics 6 permanent researchers (M.G., G. Brida, S. Castelletto (leave on absence), I. Degiovanni, M.Gramegna, I.Ruo Berchera) 5 post docs (A. Meda, E.Moreva, F. Piacentini, P.Traina, A.Shurupov); 3 PhD students (A.Avella,E.Lopaeva,G.Mingolla) Several undergraduate students, …. INRIM Quantum Optics Research program “Carlo Novero lab” Responsible: M. Genovese

3. ISTITUTO NAZIONALE DI RICERCA METROLOGICA G. Brida, I. P. Degiovanni, M. Genovese, A. Meda INRIM, Strada delle Cacce 91, I-10135 Torino, Italy S. Olivares, M. G. A. Paris Dipartimento di Fisica, Universita degli Studi di Milano, I-20133 Milano, Italy CNISM UdR Milano Statale, I-20133 Milano, Italy

4. ISTITUTO NAZIONALE DI RICERCA METROLOGICA Introduction Correlated states : important for new technologies and for deeper insight s in quantum world. A method to create correlations is the interference of light beams in linear passive devices, e.g., beamsplitters Which states? Gaussian states (coherent, thermal, squeezed) represent an important resource ; an example is the continous variable quantum information, e.g. teleportation protocol ( A. Furusawa et al. Science 282, 706 (1998))

5. ISTITUTO NAZIONALE DI RICERCA METROLOGICA Recent studies on generation of entanglement and preservation in propagation have increased the interest in effects of linear optical elements on the correlations of Gaussian states ( S. Olivares et al. Phys. Rev. Lett. 107, 170505 (2011). P. Facchi et al. Phys. Rev. A80, 062311-1 - 062311-6 (2009) ) The question is: What happens if we mix two Gaussian states in a BS? The illusionist game

6. ISTITUTO NAZIONALE DI RICERCA METROLOGICA The illusionist game

7. ISTITUTO NAZIONALE DI RICERCA METROLOGICA The illusionist game C 1,2

8. ISTITUTO NAZIONALE DI RICERCA METROLOGICA The illusionist game C 1,2

9. ISTITUTO NAZIONALE DI RICERCA METROLOGICA Is the BS present under the hat???? The illusionist game

10. ISTITUTO NAZIONALE DI RICERCA METROLOGICA The illusionist always knows the answer.. What’s the trick???? The illusionist game

11. ISTITUTO NAZIONALE DI RICERCA METROLOGICA The trick is behind the curtain…

12. ISTITUTO NAZIONALE DI RICERCA METROLOGICA

13. ISTITUTO NAZIONALE DI RICERCA METROLOGICA C 2,3 NO BS

14. ISTITUTO NAZIONALE DI RICERCA METROLOGICA C 2,3 BS

15. ISTITUTO NAZIONALE DI RICERCA METROLOGICA C 1,3 NO BS

16. ISTITUTO NAZIONALE DI RICERCA METROLOGICA C 1,3 BS

17. ISTITUTO NAZIONALE DI RICERCA METROLOGICA Outline The illusionist game, the theory : Gaussian states and linear interaction of modes, the covariance matrix and the birth or not of correlations The illusionist game, the experiment: experimental setup and correlation measurement The illusionist game, the results: the illusionist have a very low probability to make a mistake. The quantum eraser Conclusions and further applications

18. ISTITUTO NAZIONALE DI RICERCA METROLOGICA Gaussian states The most general single-mode Gaussian state: where : thermal equilibrium state squeezing operator displacement operator Given: 1) a two mode Gaussian state with density matrix 2) a billinear interaction The state is invariant under the transformation: If (and only if) the state is uncorrelated

19. ISTITUTO NAZIONALE DI RICERCA METROLOGICA The covariance matrix The covariance matrix of the Gaussian state  is: where: and First moment vector

20. ISTITUTO NAZIONALE DI RICERCA METROLOGICA When two uncorrelated Gaussian states: with covariance matrix interacts in a BS: If the states are in the same state: the beams are still uncorrelated (1) with (1)J. Eisert and M. B. Plenio, Int. J. Quantum. Inform. 1, 479 (2003); S. L. Braunstein and P. van Loock, Rev. Mod. Phys. 77, 513 (2005); A. Ferraro, S. Olivares, and M. G. A. Paris, Gaussian States in Quantum Information (Bibliopolis, Napoli, 2005). The presence of correlation was analyzed in (2) (2) S. Olivares, and M. G. A. Paris, PRL 107, 170505 and 0 0  

21. ISTITUTO NAZIONALE DI RICERCA METROLOGICA Actually, the mode 2 is correlated with mode 3: The BS acts only on mode 1 and 2: so the CM of the state is: T T

22. ISTITUTO NAZIONALE DI RICERCA METROLOGICA The same results hold in the case of multimode Gaussian states Pairwise interaction If each mode of one beam interacts with the corresponding mode of the other beam, the state is still uncorrelated…

23. ISTITUTO NAZIONALE DI RICERCA METROLOGICA The illusionist game: the experiment a b 3 2 1

24. ISTITUTO NAZIONALE DI RICERCA METROLOGICA The illusionist game: the experiment Laser source: = 532 nm Rate = 12.4 Hz CCD: 658 x 498 pixels pixel size: 10 x 10  m

25. ISTITUTO NAZIONALE DI RICERCA METROLOGICA The CCD registered one single pulse for each frame Each point on the CCD array correspond to a single mode NO BS BS very long path to be balanced! Areas: 40 x 40 pixels Number of modes ≈ 41

26. ISTITUTO NAZIONALE DI RICERCA METROLOGICA For each frame we measure: and the correlation is estimated with the second order correlation coefficient: where NB: the second order correlation coefficient is independent on the number of modes and Averaging over the frames one has the estimation of the operator

27. ISTITUTO NAZIONALE DI RICERCA METROLOGICA G We achieved pairwise superposition of modes by otimizing correlated regions in single splitted beam

28. ISTITUTO NAZIONALE DI RICERCA METROLOGICA G. Brida, I. P. Degiovanni, M. Genovese, A. Meda, S. Olivares and M. G. A. Paris, arXiv:1204.5499 [quant-ph]

29. ISTITUTO NAZIONALE DI RICERCA METROLOGICA I. Lira, Metrologia 46, L27-L28 (2009); S Olivares et al., Metrologia 49, L14 (2012). Confidence intervals @99%

30. ISTITUTO NAZIONALE DI RICERCA METROLOGICA The illusionist has a very low probability of error already taking 50 pictures! BS No BS

31. ISTITUTO NAZIONALE DI RICERCA METROLOGICA The quantum eraser H V [preliminary results]

32. ISTITUTO NAZIONALE DI RICERCA METROLOGICA We have:  suggested a novel scheme to illustrate and the counterintuitive behavior of Gaussian states:the illusionist protocol  realized the experiment with thermal light The illusionist game:  implications for decoherence control  understanding of the dynamics of correlations at BS  innovative interferometric schemes Conclusions