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We survey the state of the art for the proof of the quantum Gaussian optimizer conjectures of quantum information theory.
A characterization of poisson processes
Alfréd Rényi · 1956
Earlier work this paper cites.
Some inequalities satisfied by the quantities of information of fisher and shannon
AJ Stam · 1959
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The convolution inequality for entropy powers
Nelson M Blachman · 1965
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A simple converse for broadcast channels with additive white gaussian noise (corresp.)
Patrick P Bergmans · 1974
Earlier work this paper cites.
Inequalities in fourier analysis
William Beckner · 1975
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Sharpness in young’s inequality for convolution
John Fournier · 1977
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Thermodynamical proof of the gibbs formula for elementary quantum systems
A Lenard · 1978
Earlier work this paper cites.
The gaussian wire-tap channel
Sik K Leung-Yan-Cheong and Martin E Hellman · 1978
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Proof of an entropy conjecture of wehrl
Elliott H Lieb · 1978
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Passive states and kms states for general quantum systems
W Pusz and SL Woronowicz · 1978
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On the relation between classical and quantum-mechanical entropy
Alfred Wehrl · 1979
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Passive states for finite classical systems
J Gorecki and W Pusz · 1980
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Entropy and the central limit theorem
Andrew R Barron · 1986
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Gaussian kernels have only gaussian maximizers
Elliott H Lieb · 1990
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Information theoretic inequalities
Amir Dembo, Thomas M Cover, and Joy Thomas · 1991
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Information-theoretic measure of uncertainty due to quantum and thermal fluctuations
Arlen Anderson and Jonathan J Halliwell · 1993
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Logarithmic sobolev inequalities and contractivity properties of semigroups
Leonard Gross · 1993
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Quantum limits on bosonic communication rates
Carlton M Caves and Peter D Drummond · 1994
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A note on maximal inequality for stochastic convolutions
Erika Hausenblas and Jan Seidler · 2001
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Evaluating capacities of bosonic gaussian channels
Alexander S Holevo and Reinhard F Werner · 2001
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Analysis
E.H. Lieb and M. Loss · 2001
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A mathematical theory of communication
Claude Elwood Shannon · 2001
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Methods in Theoretical Quantum Optics
S. Barnett and P.M. Radmore · 2002
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Best constants in young’s inequality, its converse, and its generalization to more than three functions
Herm Jan Brascamp and Elliott H Lieb · 2002
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A general rearrangement inequality for multiple integrals
HJ Brascamp, Elliott H Lieb, and JM Luttinger · 2002
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The brunn-minkowski inequality
R Gardner · 2002
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Solution of Shannon’s problem on the monotonicity of entropy
Shiri Artstein, Keith M. Ball, Franck Barthe, and Assaf Naor · 2004
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Minimum output entropy of bosonic channels: a conjecture
Vittorio Giovannetti, Saikat Guha, Seth Lloyd, Lorenzo Maccone, and Jeffrey H Shapiro · 2004
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Minimum bosonic channel output entropies
Vittorio Giovannetti, Saikat Guha, Seth Lloyd, Lorenzo Maccone, Jeffrey H Shapiro, and Brent J Yen · 2004
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Structure of states which satisfy strong subadditivity of quantum entropy with equality
Patrick Hayden, Richard Jozsa, Denes Petz, and Andreas Winter · 2004
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Quantum information with continuous variables
Samuel L Braunstein and Peter Van Loock · 2005
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Gaussian States in Quantum Information
A. Ferraro, S. Olivares, and M. Paris · 2005
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Elements of Information Theory
T.M. Cover and J.A. Thomas · 2006
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Multiplicativity of p-norms of completely positive maps and the additivity problem in quantum information theory
Alexander S Holevo · 2006
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Classical information capacity of the bosonic broadcast channel
Saikat Guha and Jeffrey H Shapiro · 2007
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Classical capacity of bosonic broadcast communication and a minimum output entropy conjecture
Saikat Guha, Jeffrey H Shapiro, and Baris I Erkmen · 2007
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Thinning and the law of small numbers
Peter Harremoës, Oliver Johnson, and Ioannis Kontoyiannis · 2007
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The Brascamp-Lieb inequalities: finiteness, structure and extremals
Jonathan Bennett, Anthony Carbery, Michael Christ, and Terence Tao · 2008
Cited alongside, same era.
Multiple-user quantum information theory for optical communication channels
Saikat Guha · 2008
Cited alongside, same era.
The entropy photon-number inequality and its consequences
Saikat Guha, Baris Erkmen, and Jeffrey H Shapiro · 2008
Cited alongside, same era.
Capacity of the bosonic wiretap channel and the entropy photon-number inequality
Saikat Guha, Jeffrey H Shapiro, and Baris Erkmen · 2008
Cited alongside, same era.
A note on the p → q p\to q norms of 2-positive maps
Koenraad MR Audenaert · 2009
Cited alongside, same era.
Superadditivity of communication capacity using entangled inputs
Matthew B Hastings · 2009
Cited alongside, same era.
Gaussian optimizers and the additivity problem in quantum information theory
Alexander Semenovich Holevo · 2015
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The conditional entropy power inequality for gaussian quantum states
Robert König · 2015
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Basic Complex Analysis: A Comprehensive Course in Analysis, Part 2A:
B. Simon · 2015
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Quantum Information Processing with Finite Resources: Mathematical Foundations
M. Tomamichel · 2015
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Entropy power inequalities for qudits
Koenraad Audenaert, Nilanjana Datta, and Maris Ozols · 2016
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On a quantum entropy power inequality of audenaert, datta, and ozols
Eric A Carlen, Elliott H Lieb, and Michael Loss · 2016
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Optimal transport
Cédric Villani · 2009
Cited alongside, same era.
Monotonic convergence in an information-theoretic law of small numbers
Yaming Yu · 2009
Cited alongside, same era.
Concavity of entropy under thinning
Yaming Yu and Oliver Johnson · 2009
Cited alongside, same era.
A mass transportation approach to quantitative isoperimetric inequalities
A. Figalli, F. Maggi, and A. Pratelli · 2010
Cited alongside, same era.
Generalized minimal output entropy conjecture for one-mode gaussian channels: definitions and some exact results
Vittorio Giovannetti, Alexander S Holevo, Seth Lloyd, and Lorenzo Maccone · 2010
Cited alongside, same era.
Thinning, entropy, and the law of thin numbers
Peter Harremoës, Oliver Johnson, and Ioannis Kontoyiannis · 2010
Cited alongside, same era.
Gaussian optimizers and other topics in quantum information
Giacomo De Palma · 2016
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Passive states as optimal inputs for single-jump lossy quantum channels
Giacomo De Palma, Andrea Mari, Seth Lloyd, and Vittorio Giovannetti · 2016
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Passive states optimize the output of bosonic gaussian quantum channels
Giacomo De Palma, Dario Trevisan, and Vittorio Giovannetti · 2016
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Quantitative logarithmic Sobolev inequalities and stability estimates
Max Fathi, Emanuel Indrei, and Michel Ledoux · 2016
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Thinning, photonic beamsplitting, and a general discrete entropy power inequality
Saikat Guha, Jeffrey H Shapiro, and Raúl García-Patrón Sánchez · 2016
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Quantum Information Theory: Mathematical Foundation
M. Hayashi · 2016
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On the proof of the majorization theorem for quantum gaussian channels
Alexander S Holevo · 2016
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On the constrained classical capacity of infinite-dimensional covariant quantum channels
AS Holevo · 2016
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Corrections to “the entropy power inequality for quantum systems”
Robert König and Graeme Smith · 2016
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Gradient flow and entropy inequalities for quantum Markov semigroups with detailed balance
Eric A. Carlen and Jan Maas · 2017
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Contractivity properties of a quantum diffusion semigroup
Nilanjana Datta, Yan Pautrat, and Cambyse Rouzé · 2017
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Gaussian states minimize the output entropy of one-mode quantum gaussian channels
Giacomo De Palma, Dario Trevisan, and Vittorio Giovannetti · 2017
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Gaussian states minimize the output entropy of the one-mode quantum attenuator
Giacomo De Palma, Dario Trevisan, and Vittorio Giovannetti · 2017
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Multimode gaussian optimizers for the wehrl entropy and quantum gaussian channels
Giacomo De Palma, Dario Trevisan, and Vittorio Giovannetti · 2017
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Norms of quantum gaussian multi-mode channels
Rupert L. Frank and Elliott H. Lieb · 2017
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On the quantum gaussian optimizers conjecture in the case q = p q=p
AS Holevo · 2017
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Geometric inequalities from phase space translations
Stefan Huber, Robert König, and Anna Vershynina · 2017
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A de bruijn identity for discrete random variables
O. Johnson and S. Guha · 2017
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Capacities of quantum amplifier channels
Haoyu Qi and Mark M. Wilde · 2017
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On the minimum output entropy of single-mode phase-insensitive gaussian channels
Haoyu Qi, Mark M Wilde, and Saikat Guha · 2017
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Concentration of quantum states from quantum functional and talagrand inequalities
Cambyse Rouzé and Nilanjana Datta · 2017
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Relating relative entropy, optimal transport and fisher information: a quantum hwi inequality
Cambyse Rouzé and Nilanjana Datta · 2017
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Quantum Continuous Variables: A Primer of Theoretical Methods
A. Serafini · 2017
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Quantum Information Theory
M.M. Wilde · 2017
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Uncertainty relations with quantum memory for the wehrl entropy
Giacomo De Palma · 2018
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The wehrl entropy has gaussian optimizers
Giacomo De Palma · 2018
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Minimum error probability of quantum illumination
Giacomo De Palma and Johannes Borregaard · 2018
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The conditional entropy power inequality for quantum additive noise channels
Giacomo De Palma and Stefan Huber · 2018
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The conditional entropy power inequality for bosonic quantum systems
Giacomo De Palma and Dario Trevisan · 2018
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The one-mode quantum-limited gaussian attenuator and amplifier have gaussian maximizers
Giacomo De Palma, Dario Trevisan, and Vittorio Giovannetti · 2018
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Bounds on information combining with quantum side information
Christoph Hirche and David Reeb · 2018
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