Quantum versus classical uncertainty

S. L. Luo

Teoretičeskaâ i matematičeskaâ fizika, Tome 143 (2005) no. 2, pp. 231-240

Résumé

The uncertainty of an observable in a quantum state is usually described by variance. This description is well suited when the states are pure. But when the states are mixed, things become subtle, and the variance is a hybrid of quantum and classical uncertainties. Motivated by the notion of Fisher information in statistical inference, we establish a decomposition of the variance into quantum and classical parts. The key observation is that the Wigner–Yanase skew information (a distinguished version of quantum Fisher information) can be interpreted as a measure of quantum uncertainty. We also establish a decomposition of the conventional covariance into quantum and classical parts. The results provide a new perspective for understanding uncertainty and correlation and are used to quantify entanglement, as well as to establish a new uncertainty relation in purely quantum terms.

Détail

Keywords: uncertainty, classical uncertainty, quantum uncertainty, skew information, quantum correlation, uncertainty principle.
Mots-clés : entanglement