Hannover 2010 – scientific programme
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Q: Fachverband Quantenoptik und Photonik
Q 11: Quantum Information: Concepts and Methods II
Q 11.3: Talk
Monday, March 8, 2010, 17:00–17:15, E 214
Accuracy of the lower bound approximation for three-qubit concurrence — •Michael Siomau1 and Stephan Fritzsche2,3 — 1Max-Planck-Institut fuer Kernphysik, Postfach 103980, D-69117 Heidelberg, Germany — 2Department of Physical Sciences, P.O.Box 3000, Fin-90014 University of Oulu, Finland — 3Frankfurt Institute for Advanced Studies, D-60438 Frankfurt am Main, Germany
A proper measure for the entanglement of a mixed state is the convex roof extension to the concurrence. Unfortunately, however, the computational complexity of this entanglement measure increases with the rank r of a given density matrix with as r3 [1]. Certain approximations, such as the lower bound approximation for the concurrence [2], can significantly simplify the computations. We here investigate on particular examples the relation between the accuracy of the lower bound approximation and the rank of the density matrix. We show that for a density matrix r < 4 the lower bound for the concurrence can describe the entanglement of the state for all times. For density matrices with higher rank, in contrast, the lower bound approximation can be applied only to describe the dynamics of quasi-pure states.
[1] F. Mintert et al., Phys. Rep. 415, 207 (2005).
[2] M. Li, S.-M. Fei, Z.-X. Wang, J. Phys. A 42, 145303 (2009).