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2019

Sandwich theorems and capacity bounds for non-commutative graphs

Boreland, Gareth, Todorov, Ivan G., Winter, Andreas

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We define non-commutative versions of the vertex packing polytope, the theta convex body and the fractional vertex packing polytope of a graph, and establish a quantum version of the Sandwich Theorem of Gr\"{o}tschel, Lov\'{a}sz and Schrijver.

We define new non-commutative versions of the Lov\'{a}sz number of a graph which lead to an upper bound of the zero-error capacity of the corresponding quantum channel that can be genuinely better than the one established previously by Duan, Severini and Winter.
We define non-commutative counterparts of widely used classical graph parameters and establish their interrelation.

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D. Kretschmann, D. Schlingemann and R. F. Werner
1904
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C. E. Shannon
1956
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M.-D. Choi
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L. Lovász
1979
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P. R. Halmos
1980
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M. Grötschel, L. Lovász and A. Schrijver
1986
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I. Csiszar, J. Korner, L. Lovász, K. Marton and G. Simonyi
1990
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