Experimental Investigation of Quantum Discord in Multipartite Systems

Experimental Investigation of Quantum Discord in Multipartite Systems Vanessa Chille 1, 2, Christian Peuntinger 1, 2, Christian Gabriel 1, 2, Ladislav Mišta 3, 4, Natalia Korolkova 3, Christoph Marquardt 1, 2, Gerd Leuchs 1, 2 [1] Max Planck Institute for the Science of Light, Günther-Scharowsky-Straße 1, 91058 Erlangen, Germany [2] Institute of Optics, Information and Photonics, University Erlangen-Nuremberg, Germany [3] School of Physics and Astronomy, University of St. Andrews, North Haugh, St. Andrews KY 16 9 SS, United Kingdom [4] Department of Optics, Palacký University, 17. listopadu 50, 772 07 Olomouc, Czech Republic

Content 1) Motivation 2) Mutual Information 3) Distribution of Entanglement without Entanglement 4) Polarization Squeezing 5) Experimental Studies on Quantum Discord

Motivation Is entanglement a necessary property for quantum computation? Yes! - But only for pure quantum states, where quantum correlations coincide with entanglement. For separable mixed quantum states: quantum correlations apart from entanglement Quantum Discord quantifies these correlations.

2) Mutual Information

Mutual Information selection of the signal receipt of the signal information transferred by the communication = mutual information Quantum Information, Stephen M. Barnett, Oxford University Press, 2009

Mutual information - classical equivalent G. Adesso and A. Datta, PRL 105, 030501 (2010)

Mutual information - quantum Mutual information One-way classical correlation Quantum Discord: G. Adesso and A. Datta, PRL 105, 030501 (2010)

3) Distribution of Entanglement without Entanglement

Distribution of continuous-variable entanglement by separable Gaussian states Initially, three modes A, B and C, which form a fully mixed separable Gaussian state, are prepared. The modes A and B are finally entangled while the mode C remains always separable from the pair of modes (AB). L. Mista and N. Korolkova, Phys. Rev. A 77, 050302 (2008)

4) Polarization Squeezing

Description of polarization - in the classical domain Stokes parameters Poincaré sphere

Description of polarization - in the quantum domain Classical Stokes Parameters Quantum Stokes Operators Stokes operators do not commute, obey the SU(2) Lie algebra N. Korolkova et al. , Phys. Rev. A 65, 052306

Polarization Squeezing commutation relations for the Stokes operators Heisenberg inequalities For our experiment, we chose for example: Just as position and momentum in phase space, the Stokes parameters S 1 and S 2 can be squeezed in the dark plane S 1/S 2. R. Dong et al. , New J. Physics, 9 (410), (2007)

5) Experimental Studies on Quantum Discord

Experimental Studies Bright circularly polarized light beam, squeezed in S 1, antisqueezed in S 2.

Experimental Studies EOM, sinusoidal voltage Modulation of S 1 electric local oscillator Displacement of the squeezed state in its dark plane

Experimental Studies displacements with Gaussian distribution Gaussian mixed state

Experimental Studies the prepared state enters a quantum network Measurement of the Covariance Matrix at different points of this network Quantum Discord

take-home messages Quantum Discord… … is a measure of quantum correlations, also beyond entanglement. … may be studied using polarization squeezing, which allows a quite simple measurement scheme. … is the cause of astonishing phenonomena, such as the distribution of entanglement with separable states.