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Quantifying quantum mechanical uncertainty is vital for the increasing number of experiments that reach the uncertainty limited regime.
Zur Quantenmechanik einfacher Bewegungstypen
Earl Kennard · 1927
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Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik
Werner Heisenberg · 1927
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The uncertainty principle
Howard Percy Robertson · 1929
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Uncertainty in quantum measurements
David Deutsch · 1983
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Foundations of Quantum Mechanics I
Günther Ludwig · 1983
Earlier work this paper cites.
Generalized entropic uncertainty relations
Hans Maassen and Jos Uffink · 1988
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A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra
David Avis and Komei Fukuda · 1992
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Many-particle entanglement with bose–einstein condensates
Anders S. Sørensen, Luming Duan, Ignacio Cirac, and Peter Zoller · 2001
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Entanglement and extreme spin squeezing
Anders S. Sørensen and Klaus Mølmer · 2001
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Violation of local uncertainty relations as a signature of entanglement
Holger F. Hofmann and Shigeki Takeuchi · 2003
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Detecting quantum entanglement: entanglement witnesses and uncertainty relations
Otfried Gühne · 2004
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Entanglement detection
Otfried Gühne and Géza Tóth · 2009
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Planar quantum squeezing and atom interferometry
Qiongyi He, Shi-Guo Peng, Peter D. Drummond, and Margaret D. Reid · 2011
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The mathematical language of quantum theory: from uncertainty to entanglement
Teiko Heinosaari and Mário Ziman · 2011
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Jian Ma, Xiaoguang Wang, Chang-Pu Sun, and Franco Nori · 2011
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Twin matter waves for interferometry beyond the classical limit
Stronger uncertainty relations for all incompatible observables
Lorenzo Maccone and Arun K. Pati · 2014
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Detecting multiparticle entanglement of dicke states
Bernd Lücke, Jan Peise, Giuseppe Vitagliano, Jan Arlt, Luis Santos, Géza Tóth, and Carsten Klempt · 2014
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Uncertainty relations for angular momentum
Lars Dammeier, René Schwonnek, and Reinhard F. Werner · 2015
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Optimality of entropic uncertainty relations
Kais Abdelkhalek, René Schwonnek, Hans Maassen, Fabian Furrer, Jörg Duhme, Philippe Raynal, Berthold-Georg Englert, and Reinhard F Werner · 2015
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Bernd Lücke, Manuel Scherer, Jens Kruse, Luca Pezzé, Frank Deuretzbacher, Phillip Hyllus, Oliver Topic, Jan Peise, Wolfgang Ertmer, Jan Arlt, Luis Santos, Augusto Smerzi, and Carsten Klempt · 2011
Cited alongside, same era.
Variance-based uncertainty relations
Yichen Huang · 2012
Cited alongside, same era.
Measurement uncertainty relations
Paul Busch, Pekka Lahti, and Reinhard F. Werner · 2014
Cited alongside, same era.
Heisenberg uncertainty relation for three canonical observables
Spiros Kechrimparis and Stefan Weigert · 2014
Cited alongside, same era.
For hermitian operators we define the variance of a state ρ \rho by Δ ρ 2 ( A ) = ⟨ A 2 ⟩ ρ − ⟨ A ⟩ ρ 2 = tr ρ A 2 − ( tr ρ A ) 2 \Delta^{2}_{\rho}(A)=\langle A^{2}\rangle_{\rho}-\langle A\rangle^{2}_{\rho}=\mathop{\rm tr}\nolimits{\rho A^{2}}-(\mathop{\rm tr}\nolimits{\rho A})^{2}
Cited in the paper.
Alastair A. Abbott, Pierre-Louis Alzieu, Michael J. W. Hall, and Cyril Branciard · 2016
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Uncertainty relations for general phase spaces
Reinhard F. Werner · 2016
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Sharp uncertainty relations for number and angle
Paul Busch, Pekka Lahti, and Reinhard F. Werner · 2016
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Preparational uncertainty relations for n continuous variables
Spiros Kechrimparis and Stefan Weigert · 2016
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Measurement uncertainty for finite quantum observables
René Schwonnek, David Reeb, and Reinhard F. Werner · 2016
Later among the works it cites.