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Quantum Reports, Volume 7, Issue 3
2025 September - 15 articles
Cover Story: A simple inequality for the product of coordinate and momentum “uncertainties”, discovered in 1927 by Heisenberg (in an approximate form) and Kennard (in a strict form), is one of the “precious stones” of the quantum theory. A lot of improvements, extensions and generalizations of that inequality have been found for the past century by many authors using different definitions of “uncertainties”. This review is a collection of existing inequalities containing products or sums of variances (or their roots and powers) of non-commuting operators. Inequalities improving the uncertainty relations when additional information about a quantum system is available (for example, the correlation coefficient, the degrees of mixing or gaussianity of a quantum state) are especially interesting. View this paper
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Quantum Rep. - ISSN 2624-960X