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We study quantum versions of the Shannon capacity of graphs and non-commutative graphs.
The Zero Error Capacity of a Noisy Channel
Claude E. Shannon · 1956
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On a problem of C. E. Shannon in graph theory
M. Rosenfeld · 1967
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On the ratio of optimal integral and fractional covers
L. Lovász · 1975
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On Some Problems of Lovász Concerning the Shannon Capacity of a Graph
Willem Haemers · 1979
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On the Shannon Capacity of a Graph
László Lovász · 1979
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The Asymptotic Spectrum of Tensors and the Exponent of Matrix Multiplication
Volker Strassen · 1986
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Relative Bilinear Complexity and Matrix Multiplication
Volker Strassen · 1987
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The Asymptotic Spectrum of Tensors
Volker Strassen · 1988
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Degeneration and Complexity of Bilinear Maps: Some Asymptotic Spectra
Volker Strassen · 1991
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A Complete Classification of Quantum Ensembles Having a Given Density Matrix
Lane P. Hughston, Richard Jozsa, and William K. Wootters · 1993
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Algebraic complexity theory
Peter Bürgisser, Michael Clausen, and M. Amin Shokrollahi · 1997
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Reducibility among Combinatorial Problems
Richard M. Karp · 2001
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Optimization of Coherent Attacks in Generalizations of the BB84 Quantum Bit Commitment Protocol
Robert W. Spekkens and Terry Rudolph · 2002
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Combinatorial Optimization: Polyhedra and Efficiency
Alexander Schrijver · 2003
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Super-activation of Zero-error Capacity of Noisy Quantum Channels
Runyao Duan · 2009
Cited alongside, same era.
Entanglement-assisted Zero-error Capacity is Upper-bounded by the Lovász ϑ \vartheta Function
Salman Beigi · 2010
Cited alongside, same era.
Improving Zero-Error Classical Communication with Entanglement
Toby S. Cubitt, Debbie Leung, William Matthews, and Andreas Winter · 2010
Cited alongside, same era.
Quantum Computation and Quantum Information
Michael A. Nielsen and Isaac L. Chuang · 2010
Cited alongside, same era.
Superactivation of the Asymptotic Zero-Error Classical Capacity of a Quantum Channel
T. S. Cubitt, J. Chen, and A. W. Harrow · 2011
Cited alongside, same era.
Zero-Error Channel Capacity and Simulation Assisted by Non-Local Correlations
Quantum Homomorphisms
Laura Mančinska and David E. Roberson · 2015
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Lovász Theta Type Norms and Operator Systems
Carlos M. Ortiz and Vern I. Paulsen · 2015
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Quantum Zero-Error Source-Channel Coding and Non-Commutative Graph Theory
Dan Stahlke · 2015
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A New Property of the Lovász Number and Duality Relations between Graph Parameters
Antonio Acín, Runyao Duan, David E. Roberson, Ana Belén Sainz, and Andreas Winter · 2017
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Orthogonal representations, projective rank, and fractional minimum positive semidefinite rank: Connections and new directions
Leslie Hogben, Kevin F. Palmowski, David E. Roberson, and Simone Severini · 2017
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Quantum Information Theory
Mark M. Wilde · 2017
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T. S. Cubitt, D. Leung, W. Matthews, and A. Winter · 2011
Cited alongside, same era.
Zero-Error Communication via Quantum Channels, Noncommutative Graphs, and a Quantum Lovász Number
Runyao Duan, Simone Severini, and Andreas Winter · 2012
Cited alongside, same era.
Entanglement can Increase Asymptotic Rates of Zero-Error Classical Communication over Classical Channels
Debbie Leung, Laura Mančinska, William Matthews, Māris Ozols, and Aidan Roy · 2012
Cited alongside, same era.
Violating the Shannon Capacity of Metric Graphs with Entanglement
Jop Briët, Harry Buhrman, and Dion Gijswijt · 2013
Cited alongside, same era.
A graph-theoretic approach to network coding
Anna Blasiak · 2013
Cited alongside, same era.
New Separations in Zero-Error Channel Capacity Through Projective Kochen–Specker Sets and Quantum Coloring
L. Mančinska, G. Scarpa, and S. Severini · 2013
Cited alongside, same era.
Entanglement-assisted Zero-error Source-channel Coding
Jop Briët, Harry Buhrman, Monique Laurent, Teresa Piovesan, and Giannicola Scarpa · 2014
Cited alongside, same era.
Universal points in the asymptotic spectrum of tensors (extended abstract)
Matthias Christandl, Péter Vrana, and Jeroen Zuiddam · 2018
Closest in time.
New lower bound on the shannon capacity of C7 from circular graphs
Sven C. Polak and Alexander Schrijver · 2018
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Separation Between Quantum Lovász Number and Entanglement-Assisted Zero-Error Classical Capacity
X. Wang and R. Duan · 2018
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Algebraic complexity, asymptotic spectra and entanglement polytopes
Jeroen Zuiddam · 2018
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On a fractional version of haemers’ bound
B. Bukh and C. Cox · 2019
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The Asymptotic Spectrum of Graphs and the Shannon Capacity
Jeroen Zuiddam · 2019
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The asymptotic spectrum of LOCC transformations
A. K. Jensen and P. Vrana · 2020
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