Berlin 2012 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 10: Nonlinear Dynamics, Synchronisation and Chaos
DY 10.13: Vortrag
Dienstag, 27. März 2012, 12:45–13:00, MA 001
Measures for correlations and complexity based on exponential families — •Otfried Gühne1, Sönke Niekamp1, and Tobias Galla2 — 1Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Str. 3, D-57068 Siegen — 2Complex Systems and Statistical Physics Group, School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom
Correlations between different parts of a physical system are ubiquitous in nature. Their characterization is crucial for the study of complex systems, but also interesting from the viewpoint of quantum information theory. To quantify such correlations, measures based on the notion of exponential families have been studied [T. Kahle et al., Phys. Rev. E 79, 026201 (2009)]. The basic element of this approach is to use the distance of a probability distribution to the thermal states of k-particle Hamiltonians as a measure of the correlations in the distribution.
For the case of classical probability distributions, we show that such measures are lacking some desirable properties of correlation measures. However, we propose a modified definition which can be used to overcome this problem [T. Galla et al., arXiv:1107.1180]. In the quantum case, the probability distribution is replaced by a density matrix, but still the same type of correlation measures can be defined. We present an algorithm to compute such measures efficiently for quantum states. We also demonstrate that this approach can be used to show that certain relevant quantum states (such as the cluster states) cannot be approximated by ground states of two-body Hamiltonians.