English

The "quantum" Turan problem for operator systems

Operator Algebras 2018-02-22 v1 Combinatorics Functional Analysis Rings and Algebras Quantum Physics

Abstract

Let V be a linear subspace of M_n(C) which contains the identity matrix and is stable under Hermitian transpose. A "quantum k-clique" for V is a rank k orthogonal projection P in M_n(C) for which dim(PVP) = k^2, and a "quantum k-anticlique" is a rank k orthogonal projection for which dim(PVP) = 1. We give upper and lower bounds both for the largest dimension of V which would ensure the existence of a quantum k-anticlique, and for the smallest dimension of V which would ensure the existence of a quantum k-clique.

Cite

@article{arxiv.1802.07394,
  title  = {The "quantum" Turan problem for operator systems},
  author = {Nik Weaver},
  journal= {arXiv preprint arXiv:1802.07394},
  year   = {2018}
}

Comments

13 pages

R2 v1 2026-06-23T00:28:22.754Z