TITLE: Classical and quantum many-body correlations
SPEAKER: Stephan Weis (Independent Researcher, formerly Max-Planck-Institute for Mathematics)
ABSTRACT:
This talk begins with definitions of low-order correlations in
probability distributions induced by classes of subsystems: Monomial
maps, toric varieties, factorization, Hierarchical models (Lauritzen
1996, Geiger et al. 2006, Kahle 2010). Examples are discussed.
Hierarchical models are defined for probability distributions and for
quantum systems using the maximum-entropy principle. In a unified
classical-quantum view we explain the idea of irreducible correlation
(Linden et al. 2002, Zhou 2008) and its representation as the divergence
from a the set of thermal states of local Hamiltonians (Amari 2001, Ay
et al. 2011). We point out differences between the classical and quantum
setting (continuity, local maximizers).
This is joint work with Andreas Knauf (Erlangen), Nihat Ay (Leipzig,
Santa Fe), Ming-Jing Zhao (Beijing)