A Generalization of the Rao–Cramer Inequality
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
J. L. Hodges, Jr., E. L. Lehmann, Some applications of the Cramér-Rao inequality, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 1950, University of California Press, Berkeley and Los Angeles, 1951, 13–22
2.
C. Radhakrishna Rao, Linear statistical inference and its applications, John Wiley & Sons Inc., New York, 1965xviii+522
3.
Jacques Dixmier, Les algèbres d'opérateurs dans l'espace hilbertien (Algèbres de von Neumann), Cahiers scientifiques, Fascicule XXV, Gauthier-Villars, Paris, 1957vi+367
4.
A. S. Kholevo, Some statistical problems for quantum fields, Theory Prob. Applications, 17 (1972), 347–351
5.
Carl W. Helstrom, The minimum variance of estimates in quantum signal detection, IEEE Trans. Information Theory, IT-14 (1968), 234–242
Information & Authors
Information
Published In
Theory of Probability & Its Applications
Pages: 359 - 362
DOI: 10.1137/1118039
ISSN (online): 1095-7219
Copyright
Copyright © 1974 Society for Industrial and Applied Mathematics.
History
Submitted: 3 December 1971
Published online: 17 July 2006
Authors
Metrics & Citations
Metrics
Citations
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.
Cited By
- Thermodynamic uncertainty relation for quantum first-passage processesPhysical Review E, Vol. 105, No. 4 | 20 April 2022
- Improving sum uncertainty relations with the quantum Fisher informationPhysical Review Research, Vol. 4, No. 1 | 31 January 2022
- Uncertainty relations with the variance and the quantum Fisher information based on convex decompositions of density matricesPhysical Review Research, Vol. 4, No. 1 | 31 January 2022
- Irreversibility, Loschmidt Echo, and Thermodynamic Uncertainty RelationPhysical Review Letters, Vol. 127, No. 24 | 7 December 2021
- Moment-based superresolution: Formalism and applicationsPhysical Review A, Vol. 104, No. 3 | 15 September 2021
- Stronger uncertainty relations of mixed statesQuantum Information Processing, Vol. 19, No. 8 | 23 July 2020
- Enhancement of the metrological sensitivity limit through knowledge of the average energyPhysical Review A, Vol. 100, No. 3 | 18 September 2019
- Metrological Nonlinear Squeezing ParameterPhysical Review Letters, Vol. 122, No. 9 | 6 March 2019
- Macroscopic quantum states: Measures, fragility, and implementationsReviews of Modern Physics, Vol. 90, No. 2 | 31 May 2018
- Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum controlJournal of Physics A: Mathematical and Theoretical, Vol. 50, No. 45 | 12 October 2017
- Lower bounds on the size of general Schrödinger-cat states from experimental dataJournal of Physics A: Mathematical and Theoretical, Vol. 50, No. 11 | 20 February 2017
- Detecting Large Quantum Fisher Information with Finite Measurement PrecisionPhysical Review Letters, Vol. 116, No. 9 | 3 March 2016
- Tighter quantum uncertainty relations following from a general probabilistic boundPhysical Review A, Vol. 92, No. 1 | 2 July 2015
- Stronger Uncertainty Relations for All Incompatible ObservablesPhysical Review Letters, Vol. 113, No. 26 | 31 December 2014
- ReferencesExtreme Value Methods with Applications to Finance | 7 February 2012
- An Information Inequality for Operator Equations in Hilbert SpaceTheory of Probability & Its Applications, Vol. 26, No. 2 | 17 July 2006