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We present a polynomial time algorithm to approximately scale tensors of any format to arbitrary prescribed marginals (whenever possible).
Doubly stochastic matrices and the diagonal of a rotation matrix
Alfred Horn · 1954
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A relationship between arbitrary positive matrices and doubly stochastic matrices
R. Sinkhorn · 1964
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Concerning nonnegative matrices and doubly stochastic matrices
Richard Sinkhorn and Paul Knopp · 1967
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Linear transformations which preserve trace and positive semidefiniteness of operators
Andrzej Jamiołkowski · 1972
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Observable groups and hilbert’s fourteenth problem
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On convexity, the Weyl group and the Iwasawa decomposition
B. Kostant · 1973
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Convexity and commuting hamiltonians
M. F. Atiyah · 1982
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Convexity and commuting Hamiltonians
Michael F Atiyah · 1982
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Convexity properties of the moment mapping
V. Guillemin and S. Sternberg · 1982
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Convexity properties of the moment mapping
Victor Guillemin and Shlomo Sternberg · 1982
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Convexity properties of the moment mapping. II
Victor Guillemin and Shlomo Sternberg · 1984
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Convexity properties of the moment mapping, III
Frances Kirwan · 1984
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Cohomology of quotients in symplectic and algebraic geometry
Frances Clare Kirwan · 1984
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A stratification of the null cone via the moment map
Linda Ness and David Mumford · 1984
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The asymptotic spectrum of tensors and the exponent of matrix multiplication
Volker Strassen · 1986
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Sur l’image de l’application moment
Michel Brion · 1987
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The asymptotic spectrum of tensors
Volker Strassen · 1988
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The deflation-inflation method for certain semidefinite programming and maximum determinant completion problems
Leonid Gurvits and Peter N. Yianilos · 1998
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A deterministic strongly polynomial algorithm for matrix scaling and approximate permanents
Nati Linial, Alex Samorodnitsky, and Avi Wigderson · 1998
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Theory of linear and integer programming
Alexander Schrijver · 1998
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On the general faces of the moment polytope
Michel Brion · 1999
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The honeycomb model of gln(c) tensor products i: Proof of the saturation conjecture
A Knutson and T Tao · 1999
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Exact and asymptotic measures of multipartite pure-state entanglement
Charles H Bennett, Sandu Popescu, Daniel Rohrlich, John A Smolin, and Ashish V Thapliyal · 2000
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Coadjoint orbits, moment polytopes, and the Hilbert–Mumford criterion
Arkady Berenstein and Reyer Sjamaar · 2000
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Physical Review A
Three qubits can be entangled in two inequivalent ways · 2000
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Positivity problems and conjectures in algebraic combinatorics
Richard P Stanley · 2000
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Polynomial bounds for rings of invariants
Harm Derksen · 2001
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Moment polytopes of projective G G -varieties and tensor products of symmetric group representations
Matthias Franz · 2002
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Requirements for compatibility between local and multipartite quantum states
Sergey Bravyi · 2003
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One-qubit reduced states of a pure many-qubit state: polygon inequalities
Atsushi Higuchi, Anthony Sudbery, and Jason Szulc · 2003
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Normal forms and entanglement measures for multipartite quantum states
Frank Verstraete, Jeroen Dehaene, and Bart De Moor · 2003
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Deciding positivity of Littlewood-Richardson coefficients
Peter Bürgisser and Christian Ikenmeyer · 2012
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Computing multiplicities of lie group representations
Matthias Christandl, Brent Doran, and Michael Walter · 2012
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Tensor spaces and numerical tensor calculus
Wolfgang Hackbusch · 2012
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Tensors: geometry and applications
Joseph M Landsberg · 2012
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Algebraic complexity theory
Peter Bürgisser, Michael Clausen, and Mohammad A Shokrollahi · 2013
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Matrix analysis
Rajendra Bhatia · 2013
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Quantum state transformations and the Schubert calculus
Sumit Daftuar and Patrick Hayden · 2004
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Classical complexity and quantum entanglement
Leonid Gurvits · 2004
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Quantum marginal problem and representations of the symmetric group
Alexander Klyachko · 2004
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Combinatorial and algorithmic aspects of hyperbolic polynomials
Leonid Gurvits · 2005
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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 marginal problem and N N -representability
Alexander A Klyachko · 2006
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Peter Bürgisser and Christian Ikenmeyer · 2013
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Representation theory: a first course
William Fulton and Joe Harris · 2013
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Entanglement polytopes: multiparticle entanglement from single-particle information
Michael Walter, Brent Doran, David Gross, and Matthias Christandl · 2013
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Mark M Wilde · 2013
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Román Orús · 2014
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Convexity of momentum map, Morse index, and quantum entanglement
Adam Sawicki, Michał Oszmaniec, and Marek Kuś · 2014
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Multipartite Quantum States and their Marginals
Michael Walter · 2014
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Computational invariant theory
Harm Derksen and Gregor Kemper · 2015
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Polynomial degree bounds for matrix semi-invariants
Harm Derksen and Visu Makam · 2015
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A deterministic polynomial time algorithm for non-commutative rational identity testing
Ankit Garg, Leonid Gurvits, Rafael Oliveira, and Avi Wigderson · 2016
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Membership in moment polytopes is in NP and coNP
Peter Bürgisser, Matthias Christandl, Ketan D Mulmuley, and Michael Walter · 2017
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Universal points in the asymptotic spectrum of tensors
Matthias Christandl, Péter Vrana, and Jeroen Zuiddam · 2017
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Algorithmic and optimization aspects of brascamp-lieb inequalities, via operator scaling
Ankit Garg, Leonid Gurvits, Rafael Oliveira, and Avi Wigderson · 2017
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On vanishing of Kronecker coefficients
Christian Ikenmeyer, Ketan D Mulmuley, and Michael Walter · 2017
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Constructive non-commutative rank computation is in deterministic polynomial time
Gábor Ivanyos, Youming Qiao, and KV Subrahmanyam · 2017
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Inequalities for moment cones of finite-dimensional representations
Michele Vergne and Michael Walter · 2017
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Operator scaling via geodesically convex optimization, invariant theory and polynomial identity testing
Zeyuan Allen-Zhu, Ankit Garg, Yuanzhi Li, Rafael Oliveira, and Avi Wigderson · 2018
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Alternating minimization, scaling algorithms, and the null-cone problem from invariant theory
Peter Bürgisser, Ankit Garg, Rafael Oliveira, Michael Walter, and Avi Wigderson · 2018
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Operator scaling with specified marginals
Cole Franks · 2018
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