This article is cited in 136 papers

Quantum versus classical uncertainty

S. L. Luo<sup>ab

a</sup> Chinese Academy of Sciences
^b Carleton University

Abstract: 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.

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

Received: 29.06.2004

DOI: 10.4213/tmf1812

 English version: Theoretical and Mathematical Physics, 2005, 143:2, 681–688

Bibliographic databases:

• 
• 
• 
• 
•