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Brascamp-Lieb inequalities are entropy inequalities which have a dual formulation as generalized Young inequalities.
Unifying the Brascamp-Lieb inequality and the entropy power inequality
V. Anantharam, V. Jog, and C. Nair · 1901
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Lower bounds for the Helmholtz function
S. Golden · 1965
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Inequality with applications in statistical mechanics
C. J. Thompson · 1965
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Convex trace functions and the Wigner-Yanase-Dyson conjecture
E. H. Lieb · 1973
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A fundamental property of quantum-mechanical entropy
E. H. Lieb and M. B. Ruskai · 1973
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Proof of the strong subadditivity of quantum-mechanical entropy
E. H. Lieb and M. B. Ruskai · 1973
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Completely positive maps and entropy inequalities
G. Lindblad · 1975
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Best constants in Young’s inequality, its converse, and its generalization to more than three functions
H. J. Brascamp and E. H. Lieb · 1976
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Relative entropy and the Wigner-Yanase-Dyson-Lieb concavity in an interpolation theory
A. Uhlmann · 1977
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Generalized entropic uncertainty relations
H. Maassen and J. B. M. Uffink · 1988
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A variational expression for the relative entropy
D. Petz · 1988
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Volumes of sections of cubes and related problems
K. Ball · 1989
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Gaussian kernels have only Gaussian maximizers
E. H. Lieb · 1990
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Shadows of convex bodies
K. Ball · 1991
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Volume ratios and a reverse isoperimetric inequality
K. Ball · 1991
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An elementary introduction to modern convex geometry
K. Ball · 1997
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On a reverse form of the Brascamp-Lieb inequality
F. Barthe · 1998
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Convex geometry and functional analysis
K. Ball · 2001
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Jensen’s operator inequality
F. Hansen and G. K. Pedersen · 2003
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Jensen’s trace inequality in several variables
F. Hansen and G. K. Pedersen · 2003
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Inverse Brascamp-Lieb Inequalities along the Heat Equation
F. Barthe and D. Cordero-Erausquin · 2004
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A sharp analog of Young’s inequality on SN and related entropy inequalities
E. A. Carlen, E. H. Lieb, and M. Loss · 2004
Cited alongside, same era.
Equivalence of additivity questions in quantum information theory
P. W. Shor · 2004
Cited alongside, same era.
The Brascamp–Lieb inequalities: Finiteness, structure and extremals
J. Bennett, A. Carbery, M. Christ, and T. Tao · 2008
Cited alongside, same era.
Brascamp-Lieb inequalities for non-commutative integration
E. A. Carlen and E. H. Lieb · 2008
Cited alongside, same era.
Trace Inequalities and Quantum Entropy: An Introductory Course
E. Carlen · 2009
Cited alongside, same era.
Subadditivity of the entropy and its relation to Brascamp–Lieb type inequalities
E. A. Carlen and D. Cordero-Erausquin · 2009
Cited alongside, same era.
Brascamp-Lieb inequality and its reverse: An information theoretic view
J. Liu, T. A. Courtade, P. Cuff, and S. Verdú · 2016
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Superadditivity of quantum relative entropy for general states
A. Capel · 2017
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Gradient flow and entropy inequalities for quantum Markov semigroups with detailed balance
E. A. Carlen and J. Maas · 2017
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Entropic uncertainty relations and their applications
P. J. Coles, M. Berta, M. Tomamichel, and S. Wehner · 2017
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Information-theoretic perspectives on Brascamp-Lieb inequality and its reverse, 2017
J. Liu, T. A. Courtade, P. Cuff, and S. Verdu · 2017
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Monotonicity of the quantum relative entropy under positive maps
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Superadditivity of communication capacity using entangled inputs
M. B. Hastings · 2009
Cited alongside, same era.
The uncertainty principle in the presence of quantum memory
M. Berta, M. Christandl, R. Colbeck, J. M. Renes, and R. Renner · 2010
Cited alongside, same era.
Norm and anti-norm inequalities for positive semi-definite matrices
J.-C. Bourin and F. Hiai · 2011
Cited alongside, same era.
Information-theoretic treatment of tripartite systems and quantum channels
P. J. Coles, L. Yu, V. Gheorghiu, and R. B. Griffiths · 2011
Cited alongside, same era.
Conditional entropy for infinite-dimensional quantum systems
A. Kuznetsova · 2011
Cited alongside, same era.
Uncertainty relations from simple entropic properties
P. J. Coles, R. Colbeck, L. Yu, and M. Zwolak · 2012
Cited alongside, same era.
A. Müller-Hermes and D. Reeb · 2017
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Multivariate trace inequalities
D. Sutter, M. Berta, and M. Tomamichel · 2017
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Efficient algorithms for tensor scaling, quantum marginals, and moment polytopes
P. Bürgisser, C. Franks, A. Garg, R. Oliveira, M. Walter, and A. Wigderson · 2018
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The conditional entropy power inequality for bosonic quantum systems
G. De Palma and D. Trevisan · 2018
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Uncertainty principle for quantum channels
L. Gao, M. Junge, and N. LaRacuente · 2018
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Algorithmic and optimization aspects of Brascamp-Lieb inequalities, via operator scaling
A. Garg, L. Gurvits, R. Oliveira, and A. Wigderson · 2018
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Universal recovery maps and approximate sufficiency of quantum relative entropy
M. Junge, R. Renner, D. Sutter, M. M. Wilde, and A. Winter · 2018
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Additivity of entropic uncertainty relations
R. Schwonnek · 2018
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Approximate Quantum Markov Chains
D. Sutter · 2018
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Towards a theory of non-commutative optimization: geodesic 1st and 2nd order methods for moment maps and polytopes
P. Bürgisser, C. Franks, A. Garg, R. Oliveira, M. Walter, and A. Wigderson · 2019
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Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems
E. A. Carlen and J. Maas · 2020
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Generalizing lieb’s concavity theorem via operator interpolation
D. Huang · 2020
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Linear quantum entropy inequalities beyond strong subadditivity and their applications
L. Ligthart · 2020
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G. De Palma and D. Trevisan · 2021
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On the complexity of computing zero-error and Holevo capacity of quantum channels, 2007
S. Beigi and P. W. Shor · 2090
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