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.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 143, No. 2, pp. 231–240, May, 2005.
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Luo, S.L. Quantum versus classical uncertainty. Theor Math Phys 143, 681–688 (2005). https://doi.org/10.1007/s11232-005-0098-6
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DOI: https://doi.org/10.1007/s11232-005-0098-6