Exploiting hidden correlations the illusionist game Alice Genovese

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

INRIM Quantum Optics Research program “Carlo Novero lab” Responsible: M. Genovese 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 Ph. D students (A. Avella, E. Lopaeva, G. Mingolla) Several undergraduate students , …. 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 Ud. R Milano Statale, I-20133 Milano, Italy 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)) 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. A 80, 062311 -1 062311 -6 (2009)) The question is: What happens if we mix two Gaussian states in a BS? The illusionist game ISTITUTO NAZIONALE DI RICERCA METROLOGICA

The illusionist game ISTITUTO NAZIONALE DI RICERCA METROLOGICA

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

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

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

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

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

ISTITUTO NAZIONALE DI RICERCA METROLOGICA

NO BS C 2, 3 ISTITUTO NAZIONALE DI RICERCA METROLOGICA

BS C 2, 3 ISTITUTO NAZIONALE DI RICERCA METROLOGICA

C 1, 3 NO BS ISTITUTO NAZIONALE DI RICERCA METROLOGICA

C 1, 3 BS ISTITUTO NAZIONALE DI RICERCA METROLOGICA

Outline • The illusionist game, 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 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 ISTITUTO NAZIONALE DI RICERCA METROLOGICA

The covariance matrix of the Gaussian state r is: First moment vector where: and ISTITUTO NAZIONALE DI RICERCA METROLOGICA

When two uncorrelated Gaussian states: with covariance matrix interacts in a BS: (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) S. Olivares, and M. G. A. Paris, PRL 107, 170505 If the states are in the same state: the beams are still uncorrelated ISTITUTO NAZIONALE DI RICERCA METROLOGICA and s 0 0 s

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

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

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

The illusionist game: the experiment Laser source: l = 532 nm Rate = 12. 4 Hz CCD: 658 x 498 pixels pixel size: 10 x 10 mm ISTITUTO NAZIONALE DI RICERCA METROLOGICA

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

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

G. Brida, I. P. Degiovanni, M. Genovese, A. Meda, S. Olivares and M. G. A. Paris, ar. Xiv: 1204. 5499 [quant-ph] ISTITUTO NAZIONALE DI RICERCA METROLOGICA

Confidence intervals @99% I. Lira, Metrologia 46, L 27 -L 28 (2009); S Olivares et al. , Metrologia 49, L 14 (2012). ISTITUTO NAZIONALE DI RICERCA METROLOGICA

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

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

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