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Three - color entanglement and disentanglement for partial losses

Three - color entanglement and disentanglement for partial losses. Antonio Coelho 1 , Felippe Barbosa 1 , Katiuscia N. Cassemiro 2,3 , Alessandro S. Villar 2,3 , Marcelo Martinelli 1 , and Paulo Nussenzveig 1. 1 University of São Paulo 2 Max Planck Institute for the Science of Light

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Three - color entanglement and disentanglement for partial losses

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  1. Three-colorentanglement and disentanglement for partial losses Antonio Coelho1, Felippe Barbosa1, Katiuscia N. Cassemiro2,3, Alessandro S. Villar2,3, Marcelo Martinelli1, and Paulo Nussenzveig1 1University of São Paulo 2Max Planck Institute for the Science of Light 3University of Erlangen-Nürnberg

  2. The Optical Parametric Oscillator (OPO)

  3. The OPO Crystal 1062 nm / 1066 nm 532 nm OPO Signal Pump Idler Pump generates twin photons (signal and idler) inside a cavity. Strong intensity correlations in the output beams. OPO Signal Pump Idler Correlation measured by the subtraction of detector photocurrents.

  4. Sum of variances criterion Separability  • Duan separability criterion: A. S. Villar et al., PRL 95, 243603 (2005) “Twin Beams” P. van Loock & A. Furusawa, Phys. Rev. A 67, 052315 (2003).

  5. p1 p2 Y Y |a | |a | Y=q q1 q2 f f X X a0=|a0| X=p Y q- p+ p- |a+ | q+ f+ X Signal Idler Pump Energy Conservation w1 + w2 = w0 dI1 - dI2 = 0 dj1 + dj2 = dj0 Intensity Correlation Phase Anti-correlation Experiment: A. Heidmann et al., Phys. Rev. Lett.59, 2555 (1987) Theory: M. D. Reid and P. D. Drummond, Phys. Rev. Lett.60, 2731 (1988) Signal + Idler Signal - Idler

  6. But: where has the Tripartite Entanglement gone?!? Classical noise: Phonons!… Lowering the temperature... Aha! PRA 79 063816 (2009)

  7. PPT entanglement criterion Symplectic eigenvalues: Positivity under Partial Transposition (PPT) : Peres PRL77, 1413 (1996) • For separable systems, the operator obtained under partial transposition must have positive semi-definite eigenvalues. • Continuous variables: Simon PRL84, 2726 (2000) Quantum properties of Gaussian states are completely characterized by their second-order moments (variances and covariances), which can be conveniently organized in the form of a covariance matrix. separable state PT

  8. Pump beam OPO (@ -20ºC) PRA 79 063816 (2009) Phase measurement A. S. Villar, Am. J. Phys. 76, 922 (2008)

  9. Does not God play dice?

  10. Disentanglement for partial loss No more “surprises”?

  11. Loss of entanglement for partial loss No more “surprises”?

  12. Disentanglement for a simpler state:Bipartite & Gaussian Tighter conditions for exchanging of quantum information! F. A. S. Barbosa et al., Nature Photonics submitted…

  13. Conclusions • We performed the measurement of tripartite entanglement among three bright beams of light, all of different wavelengths. • Partial-loss disentanglement : much is still unknown about the nature and dynamics of quantum entanglement. • Understanding the simplest situations should help us to deal with more complex settings, involving a larger number of entangled parties.

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