Download Quantum Discord

Experimental Investigation of
Quantum Discord in Multipartite Systems
Vanessa Chille1,2, Christian Peuntinger1,2, Christian Gabriel1,2,
Ladislav Mišta3,4, Natalia Korolkova3, Christoph Marquardt1,2,
Gerd Leuchs1,2
[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 KY16 9SS, 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
H ( A)
H ( B)
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
H ( B)
H ( A)
H ( A | B)
H ( A, B)
H ( B | A)
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 S1 and S2 can be squeezed
in the dark plane S1/S2 .
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 S1,
antisqueezed in S2.
Experimental Studies
EOM,
sinusoidal voltage
Modulation of S1
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.