2016/04/01 by Zhen‐Peng Xu, Jing‐Ling Chen, Xu, Zhen-Peng +1
Computer Science · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Inequalities and Applications #Matrix Theory and Algorithms #Quantum Mechanics and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.1604.00154
openalex publication_date 2016/04/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Quantum contextuality is usually revealed by the non-contextual inequality, which can always be associated with an exclusivity graph. The quantum upper bound of the inequality is nothing but the Lovász number of the graph. In this work, we show that if there is a Lovász-optimum orthogonal representation realized in the d-dimensional complex Hilbert space, then there always exists a corresponding Lovász-optimum orthogonal representation in the (2d-1)-dimensional real Hilbert space. This in turn completes the proof that the Lovász-optimum orthogonal representation for any exclusivity graph can always be realized in the real Hilbert space of suitable dimension.