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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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slide1

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

slide4

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.

slide5

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).

slide6

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

slide7

But: where has the Tripartite Entanglement gone?!?

Classical noise: Phonons!…

Lowering the temperature... Aha!

PRA 79 063816 (2009)

slide8

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

slide9

Pump beam

OPO (@ -20ºC)

PRA 79 063816 (2009)

Phase measurement

A. S. Villar, Am. J. Phys. 76, 922 (2008)

slide12

Disentanglement for partial loss

No more “surprises”?

slide14

Disentanglement for a simpler state:Bipartite & Gaussian

Tighter conditions for exchanging of quantum information!

F. A. S. Barbosa et al., Nature Photonics submitted…

slide15

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.