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In the quantum state tomography problem, one wishes to estimate an unknown $d$-dimensional mixed quantum state $\rho$, given few copies.
Some methods applicable to identities and inequalities of symmetric algebraic functions of n n letters
Robert Muirhead · 1902
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Quelques remarques sur une construction de Schensted
Marcel-Paul Schützenberger · 1963
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An extension of Schensted’s theorem
Curtis Greene · 1974
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Nets of Grassmann manifold and orthogonal group
Stanisław Szarek · 1982
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Asymptotic of the largest and the typical dimensions of irreducible representations of a symmetric group
Anatoly Vershik and Sergei Kerov · 1985
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Symmetry properties of product states for the system of N N n n -level atoms
Robert Alicki, Sławomir Rudnicki, and Sławomir Sadowski · 1988
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Young tableaux: with applications to representation theory and geometry
William Fulton · 1997
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Random words, Toeplitz determinants and integrable systems I
Alexander Its, Craig Tracy, and Harold Widom · 2001
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Estimating the spectrum of a density operator
Michael Keyl and Reinhard Werner · 2001
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The symmetric group: representations, combinatorial algorithms, and symmetric functions
Bruce Sagan · 2001
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Quantum universal variable-length source coding
Masahito Hayashi and Keiji Matsumoto · 2002
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Conditioned random walks and the RSK correspondence
Neil O’Connell · 2003
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Applications of coherent classical communication and the Schur transform to quantum information theory
Aram Harrow · 2005
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A digest on representation theory of the symmetric group
Koenraad Audenaert · 2006
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The spectra of quantum states and the Kronecker coefficients of the symmetric group
Matthias Christandl and Graeme Mitchison · 2006
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Quantum state estimation and large deviations
Michael Keyl · 2006
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Focus on quantum tomography
Konrad Banaszek, Marcus Cramer, and David Gross · 2013
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http://mathoverflow.net/a/140739/658
Mark van Leeuwen, 2013 · 2013
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Low rank matrix recovery from rank one measurements
Richard Kueng, Holger Rauhut, and Ulrich Terstiege · 2014
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The surprising mathematics of longest increasing subsequences
Dan Romik · 2014
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Rayleigh theorem, projection of orbital measures and spline functions
Jacques Faraut · 2015
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http://dabacon.org/pontiff/?p=10785
Aram Harrow, 2015 · 2015
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Weak Fourier-Schur sampling, the hidden subgroup problem, and the quantum collision problem
Andrew Childs, Aram Harrow, and Paweł Wocjan · 2007
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Inequalities for symmetric means
Allison Cuttler, Curtis Greene, and Mark Skandera · 2011
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Inequalities: theory of majorization and its applications
Albert W Marshall, Ingram Olkin, and Barry Arnold · 2011
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Quantum tomography via compressed sensing: error bounds, sample complexity and efficient estimators
Steven Flammia, David Gross, Yi-Kai Liu, and Jens Eisert · 2012
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Sample-optimal tomography of quantum states
Jeongwan Haah, Aram Harrow, Zhengfeng Ji, Xiaodi Wu, and Nengkun Yu · 2015
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Quantum spectrum testing
Ryan O’Donnell and John Wright · 2015
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On inequalities for normalized Schur functions
Suvrit Sra · 2015
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http://www.cs.cmu.edu/~jswright , 2015
2015
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