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We investigate quantum tomography in scenarios where prior information restricts the state space to a smooth manifold of lower dimensionality.
Immersions of manifolds
Morris W Hirsch · 1959
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Characteristic classes and homogeneous spaces, ii
Armand Borel and Friedrich Hirzebruch · 1959
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Quelques théorèmes de non-plongement pour les variétés différentiables
Michael F Atiyah and Friedrich Hirzebruch · 1959
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Immersions and embeddings of manifolds
M.F. Atiyah · 1962
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Elliptische Differentialoperatoren und Ganzzahligkeitssätze für charakteristische Zahlen
Karl Heinz Mayer · 1965
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Immersing projective spaces
R James Milgram · 1967
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Foundations of differentiable manifolds and Lie groups
Frank W Warner · 1971
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Some embeddings of lie groups in euclidean space
Elmer Rees · 1971
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Characteristic classes
John Willard Milnor and James D Stasheff · 1974
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Differential topology
Morris W Hirsch · 1976
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Phase retrieval in crystallography and optics
R. Millane · 1990
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Pauli problem for a spin of arbitrary length: A simple method to determine its wave function
Stefan Weigert · 1992
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Obstructions to immersions of projective stiefel manifolds
Nelza Elisabete Barufatti · 1994
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Operational quantum physics
Paul Busch, Marian Grabowski, and Pekka Johannes Lahti · 1995
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Topological methods in algebraic geometry
Friedrich Hirzebruch · 1995
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C*-algebras by example
Kenneth R Davidson · 1996
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Reconstructing the density matrix of a spin s through Stern-Gerlach measurements
Jean-Pierre Amiet and Stefan Weigert · 1998
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Reconstructing the density matrix of a spin s through Stern-Gerlach measurements: II
Jean-Pierre Amiet and Stefan Weigert · 1999
Cited alongside, same era.
Cohomology of complex projective stiefel manifolds
L Astey, S Gitler, E Micha, and G Pastor · 1999
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On the dimension of subspaces with bounded schmidt rank
Toby Cubitt, Ashley Montanaro, and Andreas Winter · 2008
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Quantum state tomography via compressed sensing
David Gross, Yi-Kai Liu, Steven T Flammia, Stephen Becker, and Jens Eisert · 2010
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Recovering low-rank matrices from few coefficients in any basis
David Gross · 2011
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Probabilistic and statistical aspects of quantum theory
Alexander S Holevo · 2011
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Quantum tomography via compressed sensing: error bounds, sample complexity and efficient estimators
Steven T Flammia, David Gross, Yi-Kai Liu, and Jens Eisert · 2012
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Quantum tomography under prior information
Teiko Heinosaari, Luca Mazzarella, and Michael M Wolf · 2013
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Parallelizability of complex projective stiefel manifolds
L. Astey, S. Gitler, E. Micha, and G. Pastor · 2000
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Lower bounds for the immersion dimension of homogeneous spaces
Markus Walgenbach · 2001
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Multivariate simultaneous approximation
Thomas Bagby, Len Bos, and Norman Levenberg · 2002
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Vector bundles and k-theory
Allen Hatcher · 2003
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Pure-state informationally complete and “really” complete measurements
J Finkelstein · 2004
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Scalable multiparticle entanglement of trapped ions
H Häffner, W Hänsel, CF Roos, J Benhelm, et al · 2005
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Tasks and premises in quantum state determination
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A partial derandomization of phaselift using spherical designs
David Gross, Felix Krahmer, and Richard Kueng · 2014
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Process tomography for unitary quantum channels
Nathaniel Johnston Gus Gutoski · 2014
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Quantum process tomography of unitary and near-unitary maps
Ivan H. Deutsch Charles H. Baldwin, Amir Kalev · 2014
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Expanding the principle of local distinguishability
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