Geodesic
Construction of anticliques for noncommutative operator graphs
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 45, Tome 456 (2017), pp. 5-15 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Anticliques are constructed for noncommutative operator graphs generated by generalized Pauli matrices. It is shown that the use of entangled states for construction of a subspace $K$ enables one to considerably increase the dimension of a noncommutative operator graph for which the projection onto $K$ is an anticlique. 
@article{ZNSL_2017_456_a0,
     author = {G. G. Amosov and A. S. Mokeev},
     title = {Construction of anticliques for noncommutative operator graphs},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--15},
     year = {2017},
     volume = {456},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_456_a0/}
}
TY  - JOUR
AU  - G. G. Amosov
AU  - A. S. Mokeev
TI  - Construction of anticliques for noncommutative operator graphs
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2017
SP  - 5
EP  - 15
VL  - 456
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2017_456_a0/
LA  - ru
ID  - ZNSL_2017_456_a0
ER  - 
%0 Journal Article
%A G. G. Amosov
%A A. S. Mokeev
%T Construction of anticliques for noncommutative operator graphs
%J Zapiski Nauchnykh Seminarov POMI
%D 2017
%P 5-15
%V 456
%U http://geodesic.mathdoc.fr/item/ZNSL_2017_456_a0/
%G ru
%F ZNSL_2017_456_a0
G. G. Amosov; A. S. Mokeev. Construction of anticliques for noncommutative operator graphs. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 45, Tome 456 (2017), pp. 5-15. http://geodesic.mathdoc.fr/item/ZNSL_2017_456_a0/

[1] M. D. Choi, E. G. Effros, “Injectivity and operator spaces”, J. Funct. Anal., 24 (1977), 156–209 | DOI | MR | Zbl

[2] R. Duan, S. Severini, A. Winter, “Zero-error communication via quantum channels, noncommutative graphs and a quantum Lovasz theta function”, IEEE Trans. Inf. Theory, 59 (2013), 1164–1174 ; arXiv: 1002.2514 | DOI | MR | Zbl

[3] N. Weaver, “Quantum relations”, Mem. Amer. Math. Soc., 215, no. 1010, 2012, v-vi, 81–140 | MR

[4] E. Knill, R. Laflamme, “Theory of quantum error-correcting codes”, Phys. Rev. A, 55 (1997), 900–911 | DOI | MR

[5] E. Knill, R. Laflamme, L. Viola, “Theory of quantum error correction for general noise”, Phys. Rev. Lett., 84 (2000), 2525–2528 | DOI | MR | Zbl

[6] N. Weaver, A “quantum” Ramsey theorem for operator systems, 2016, arXiv: 1601.01259 | MR

[7] H. Tverberg, “A generalization of Radon's theorem”, J. London Math. Soc., 41 (1966), 123–128 | DOI | MR | Zbl

[8] H. Tverberg, “A generalization of Radon's theorem, II”, Bull. Austral. Math. Soc., 24 (1981), 321–325 | DOI | MR | Zbl

[9] P. Shor, “Scheme for reducing decoherence in quantum computer memory”, Phys. Rev. A, 52 (1995), R2493–R2496 | DOI

[10] U. Haagerup, “Orthogonal maximal abelian $*$-subalgebras of the $n\times n$ matrices and cyclic $n$-roots”, Operator Algebras and Quantum Field Theory (Rome, 1996), International Press, Cambridge, MA, 1997, 296–322 | MR | Zbl