From asymmetry to correlations

Symmetry, as well as the dual concept of asymmetry, are essential, powerful and ubiquitous in physics and nature. Motivated by the original Wigner-Yanase skew information and its extension by Dyson (Wigner E. P. and Yanase M. M., Proc. Natl. Acad. Sci. U.S.A., 49 (1963) 910), which quantifies the information content of a quantum state skew to a conserved observable and may be reinterpreted as asymmetry of a state with respect to an observable, we address the issue of quantifying asymmetry and symmetry of states with respect to Lie groups and Lie algebras. We elucidate that correlations arise naturally from the difference between asymmetries of global and local states. This provides a fundamental insight into correlations. The idea is further illustrated by several examples.